From Adam Clarke for "Everywhere.":

Every where - In every place. That they should always have a praying heart, and this will ever find a praying place. This may refer to a Jewish superstition. They thought, at first, that no prayer could be acceptable that was not offered at the temple at Jerusalem; afterward this was extended to the Holy Land; but, when they became dispersed among the nations, they built oratories or places of prayer, principally by rivers and by the seaside; and in these they were obliged to allow that public prayer might be legally offered, but nowhere else. In opposition to this, the apostle, by the authority of Christ, commands men to pray everywhere; that all places belong to God’s dominions; and, as he fills every place, in every place he may be worshipped and glorified. As to ejaculatory prayer, they allowed that this might be performed standing, sitting, leaning, lying, walking by the way, and during their labor. Beracoth, fol. xi. 1. And yet in some other places they teach differently. ~Adam Clarke

Lifting up holy hands - To lift up the hands denotes supplication, as it was a common attitude of prayer to spread abroad the hands toward heaven; compare Psalm 68:31; Exodus 9:29, Exodus 9:33; 1 Kings 8:22; 2 Chronicles 6:12-13; Isaiah 1:15. “Holy hands” here, mean hands that are not defiled by sin, and that have not been employed for any purpose of iniquity. The idea is, that when men approach God they should do it in a pure and holy manner.

Quoted verses:

Psalm 68:31
Princes shall come out of Egypt; Ethiopia shall soon stretch out her hands unto God.

Exodus 9:29
And Moses said unto him, As soon as I am gone out of the city, I will spread abroad my hands unto the LORD; and the thunder shall cease, neither shall there be any more hail; that thou mayest know how that the earth is the LORD'S.

Exodus 9:33
And Moses went out of the city from Pharaoh, and spread abroad his hands unto the LORD: and the thunders and hail ceased, and the rain was not poured upon the earth.

1 Kings 8:22
And Solomon stood before the altar of the LORD in the presence of all the congregation of Israel, and spread forth his hands toward heaven:

2 Chronicles 6:12-13
12 And he stood before the altar of the LORD in the presence of all the congregation of Israel, and spread forth his hands:
13 For Solomon had made a brasen scaffold, of five cubits long, and five cubits broad, and three cubits high, and had set it in the midst of the court: and upon it he stood, and kneeled down upon his knees before all the congregation of Israel, and spread forth his hands toward heaven,

Isaiah 1:15
And when ye spread forth your hands, I will hide mine eyes from you: yea, when ye make many prayers, I will not hear: your hands are full of blood. ~Barnes Notes

From the Adam Clarke:

Lifting up holy hands - It was a common custom, not only among the Jews, but also among the heathens, to lift up or spread out their arms and hands in prayer. It is properly the action of entreaty and request; and seems to be an effort to embrace the assistance requested. But the apostle probably alludes to the Jewish custom of laying their hands on the head of the animal which they brought for a sin-offering, confessing their sins, and then giving up the life of the animal as an expiation for the sins thus confessed. And this very notion is conveyed in the original term, from to lift up, and, upon or over. This shows us how Christians should pray. They should come to the altar; set God before their eyes; humble themselves for their sins; bring as a sacrifice the Lamb of God; lay their hands on this sacrifice; and by faith offer it to God in their souls’ behalf, expecting salvation through his meritorious death alone. ~Adam Clarke

Without wrath - That is, without the intermingling of any evil passion; with a calm, peaceful, benevolent mind. There should be nothing of the spirit of contention; there should be no anger toward others; the suppliant should be at peace with all people. It is impossible for a man to pray with comfort, or to suppose that his prayers will be heard, if he cherishes anger. The following exquisite and oft-quoted passage from Jeremy Taylor, is a more beautiful and striking illustration of the effect of anger in causing our prayers to return unanswered than was probably ever penned by anyone else. Nothing could be more true, beautiful, and graphic. “Anger sets the house on fire, and all the spirits are busy upon trouble, and intend propulsion, defense, displeasure, or revenge. It is a short madness, and an eternal enemy to discourse and a fair conversation; it intends its own object with all the earnestness of perception or activity of design, and a quicker motion of a too warm and distempered blood; it is a fever in the heart, and a calenture in the head, and a fire in the face, and a sword in the band, and a fury all over; and therefore can never suffer a man to be in a disposition to pray. For prayer is the peace of our spirit, the stillness of our thoughts, the evenness of recollection, the seat of meditation, the rest of our cares, and the calm of our tempest; prayer is the issue of a quiet mind, of untroubled thoughts; it is the daughter of charity and the sister of meekness; and he that prays to God with an angry, that is, with a troubled and discomposed spirit, is like him that retires into a battle to meditate, and sets up his closet in the out-quarters of an army, and chooses a frontier garrison to be wise in.

Anger is a perfect alienation of the mind from prayer, and therefore is contrary to that attention which presents our prayers in a right line to God. ~Barnes Notes

From the Adam Clarke:

Without wrath - Having no vindictive feeling against any person; harbouring no unforgiving spirit, while they are imploring pardon for their own offenses. The holy hands refer to the Jewish custom of washing their hands before prayer; this was done to signify that they had put away all sin, and purposed to live a holy life. ~Adam Clarke

From the Geneva Bible Translation Notes:

without wrath - Without the griefs and offences of the mind, which hinder us from calling upon God with a good conscience. ~Geneva Bible Translation Notes

And doubting - This word, as used here, does not mean, as our translation would seem to imply, that we are to come before God without any doubts of our own piety, or in the exercise of perfect faith. The word used dialogismos means, properly, computation, adjustment of accounts; then reflection, thought; then reasoning, opinion; then debate, contention, strife; Luke 9:46; Mark 9:33-34; Philippians 2:14. This is the sense evidently in this place. They were not to approach God in prayer in the midst of clamorous disputings and angry contentions. They were not to come when the mind was heated with debate, and irritated by strife for victory. Prayer was to be offered in a calm, serious, sober state of mind, and they who engaged in polemical strife, or in warm contention of any kind, are little fitted to unite in the solemn act of addressing God. How often do even good people, holding different views on the disputed points of religious doctrine, suffer their minds to become so excited, and their temper so ruffled, that they are conscious they are in an unfit state of mind to approach the throne of grace together! That theological debate has gone too far; that strife for victory has become too warm, when the disputants are in such a state of mind that they cannot unite in prayer; when they could not cease their contentions, and with a calm and proper spirit, bow together before the throne of grace.

Quoted verses:

Luke 9:46
Then there arose a reasoning among them, which of them should be greatest.

Mark 9:33-34
3 And he came to Capernaum: and being in the house he asked them, What was it that ye disputed among yourselves by the way?
34 But they held their peace: for by the way they had disputed among themselves, who should be the greatest.

Philippians 2:14
Do all things without murmurings and disputings: ~Barnes Notes

From the Adam Clarke:

And doubting - reasonings, dialogues. Such as are often felt by distressed penitents and timid believers; faith, hope, and unbelief appearing to hold a disputation and controversy in their own bosoms, in the issue of which unbelief ordinarily triumphs. The apostle therefore wills them to come, implicitly relying on the promises of God, and the sacrifice and mediation of Jesus Christ. ~Adam Clarke

The Geneva Bible Translation Notes:

and doubting - Doubting, which is against faith; (James 1:6).

Quoted verse:

James 1:6
But let him ask in faith, nothing wavering. For he that wavereth is like a wave of the sea driven with the wind and tossed. ~Geneva Bible Translation Notes

Let us finish in the Treasury of Scriptural Knowledge:

For, "I will therefore that men":

1 Timothy 5:14   ...a command
I will therefore that the younger women marry, bear children, guide the house, give none occasion to the adversary to speak reproachfully.

For, "pray everywhere": ...these scriptures making note of the places one could pray...everywhere

Psalm 130:1-2
1 Out of the depths have I cried unto thee, O LORD.
2 Lord, hear my voice: let thine ears be attentive to the voice of my supplications.

Lamentations 3:55-56
55 I called upon thy name, O LORD, out of the low dungeon.
56 Thou hast heard my voice: hide not thine ear at my breathing, at my cry.

Jonah 2:1-2
1 Then Jonah prayed unto the LORD his God out of the fish's belly,
2 And said, I cried by reason of mine affliction unto the LORD, and he heard me; out of the belly of hell cried I, and thou heardest my voice.

John 4:23-25 ...this verse speaking to why we can pray anywhere
23 But the hour cometh, and now is, when the true worshippers shall worship the Father in spirit and in truth: for the Father seeketh such to worship him.
24 God is a Spirit: and they that worship him must worship him in spirit and in truth.
25 The woman saith unto him, I know that Messias cometh, which is called Christ: when he is come, he will tell us all things.

Acts 21:5
And when we had accomplished those days, we departed and went our way; and they all brought us on our way, with wives and children, till we were out of the city: and we kneeled down on the shore, and prayed.

For, "lifting up holy hands":

Psalm 26:6
I will wash mine hands in innocency: so will I compass thine altar, O LORD:

Psalm 66:18
If I regard iniquity in my heart, the Lord will not hear me:

Proverbs 15:8
The sacrifice of the wicked is an abomination to the LORD: but the prayer of the upright is his delight.

Proverbs 21:27
The sacrifice of the wicked is abomination: how much more, when he bringeth it with a wicked mind?

Hebrews 10:22 ...showing how we make our hands holy.
Let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience, and our bodies washed with pure water.

James 4:8
Draw nigh to God, and he will draw nigh to you. Cleanse your hands, ye sinners; and purify your hearts, ye double minded.

1 John 3:20-22
20 For if our heart condemn us, God is greater than our heart, and knoweth all things.
3:21 Beloved, if our heart condemn us not, then have we confidence toward God.
3:22 And whatsoever we ask, we receive of him, because we keep his commandments, and do those things that are pleasing in his sight.

For, "without wrath":

Matthew 5:22-24
22 But I say unto you, That whosoever is angry with his brother without a cause shall be in danger of the judgment: and whosoever shall say to his brother, Raca, shall be in danger of the council: but whosoever shall say, Thou fool, shall be in danger of hell fire.
23 Therefore if thou bring thy gift to the altar, and there rememberest that thy brother hath ought against thee;
24 Leave there thy gift before the altar, and go thy way; first be reconciled to thy brother, and then come and offer thy gift.

Matthew 5:44
But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you;

Matthew 6:14-15
14 For if ye forgive men their trespasses, your heavenly Father will also forgive you:
15 But if ye forgive not men their trespasses, neither will your Father forgive your trespasses.

1 Peter 3:7
Likewise, ye husbands, dwell with them according to knowledge, giving honour unto the wife, as unto the weaker vessel, and as being heirs together of the grace of life; that your prayers be not hindered.

For, "and doubting":

Matthew 21:21
Jesus answered and said unto them, Verily I say unto you, If ye have faith, and doubt not, ye shall not only do this which is done to the fig tree, but also if ye shall say unto this mountain, Be thou removed, and be thou cast into the sea; it shall be done.

Mark 11:23-24
23 For verily I say unto you, That whosoever shall say unto this mountain, Be thou removed, and be thou cast into the sea; and shall not doubt in his heart, but shall believe that those things which he saith shall come to pass; he shall have whatsoever he saith.
24 Therefore I say unto you, What things soever ye desire, when ye pray, believe that ye receive them, and ye shall have them.

See the sermon, "Tell It to the Mountain"

James 1:6-8
6 But let him ask in faith, nothing wavering. For he that wavereth is like a wave of the sea driven with the wind and tossed.
7 For let not that man think that he shall receive any thing of the Lord.
8 A double minded man is unstable in all his ways.