Doesn’t the New Testament allow us now to eat unclean food?

This passage below is used to claim that unclean meat is not unclean anymore, from the quotes “and he became very hungry”, “Rise, Peter; kill, and eat” and “what God hath cleansed, that call not thou common”:

Acts 10:9-15 King James Version (KJV)
9 On the morrow, as they went on their journey, and drew nigh unto the city, Peter went up upon the housetop to pray about the sixth hour:
10 And he became very hungry, and would have eaten: but while they made ready, he fell into a trance,
11 And saw heaven opened, and a certain vessel descending upon him, as it had been a great sheet knit at the four corners, and let down to the earth:
12 Wherein were all manner of fourfooted beasts of the earth, and wild beasts, and creeping things, and fowls of the air.
13 And there came a voice to him, Rise, Peter; kill, and eat.
14 But Peter said, Not so, Lord; for I have never eaten any thing that is common or unclean.
15 And the voice spake unto him again the second time, What God hath cleansed, that call not thou common.

However, if readers of the passage would bother to keep reading the chapter, they would come across that “this was done thrice”, and further it reads “Behold, three men seek thee”, with the conclusion from Peters own words saying “God hath shewed me that I should not call any man common or unclean”:

Acts 10:17-20,28 King James Version (KJV)
16 This was done thrice: and the vessel was received up again into heaven.
17 Now while Peter doubted in himself what this vision which he had seen should mean, behold, the men which were sent from Cornelius had made enquiry for Simon’s house, and stood before the gate,
18 And called, and asked whether Simon, which was surnamed Peter, were lodged there.
19 While Peter thought on the vision, the Spirit said unto him, Behold, three men seek thee.
20 Arise therefore, and get thee down, and go with them, doubting nothing: for I have sent them.
28 And he said unto them, Ye know how that it is an unlawful thing for a man that is a Jew to keep company, or come unto one of another nation; but God hath shewed me that I should not call any man common or unclean.

1 Timothy chapter 4 is often used as evidence for eating unclean meat, but the verse is referring to “commanding to abstain from meats”:

1 Timothy 4:3-5 King James Version (KJV)
3 Forbidding to marry, and commanding to abstain from meats, which God hath created to be received with thanksgiving of them which believe and know the truth.
4 For every creature of God is good, and nothing to be refused, if it be received with thanksgiving:
5 For it is sanctified by the word of God and prayer.

Similarly, in Romans it illustrates an argument between one that “may eat all things” referring to more than just vegetables, and another who “eateth herbs” meaning just vegetables, but that both should not “despise” or “judge” each other for their choices they make:

Romans 14:2-4 King James Version (KJV)
2 For one believeth that he may eat all things: another, who is weak, eateth herbs.
3 Let not him that eateth despise him that eateth not; and let not him which eateth not judge him that eateth: for God hath received him.
4 Who art thou that judgest another man’s servant? to his own master he standeth or falleth. Yea, he shall be holden up: for God is able to make him stand.

Romans further says “to him that esteemeth any thing to be unclean, to him it is unclean” but “if thy brother be grieved with thy meat” to “destroy not him with thy meat” but to “follow after the things which make for peace”:

Romans 14:14-23 King James Version (KJV)
14 I know, and am persuaded by the Lord Jesus, that there is nothing unclean of itself: but to him that esteemeth any thing to be unclean, to him it is unclean.
15 But if thy brother be grieved with thy meat, now walkest thou not charitably. Destroy not him with thy meat, for whom Christ died.
16 Let not then your good be evil spoken of:
17 For the kingdom of God is not meat and drink; but righteousness, and peace, and joy in the Holy Ghost.
18 For he that in these things serveth Christ is acceptable to God, and approved of men.
19 Let us therefore follow after the things which make for peace, and things wherewith one may edify another.
20 For meat destroy not the work of God. All things indeed are pure; but it is evil for that man who eateth with offence.
21 It is good neither to eat flesh, nor to drink wine, nor any thing whereby thy brother stumbleth, or is offended, or is made weak.
22 Hast thou faith? have it to thyself before God. Happy is he that condemneth not himself in that thing which he alloweth.
23 And he that doubteth is damned if he eat, because he eateth not of faith: for whatsoever is not of faith is sin.

Another verse used to claim that unclean meat is now clean is quoted saying “let no man therefore judge you in meat”, but this is not referring to unclean meat but food of the feasts and festivals “which are a shadow of things to come”:

Colossians 2:16-17 King James Version (KJV)
16 Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath days:
17 Which are a shadow of things to come; but the body is of Christ.

The word “meat” in the Bible does not actually refer to meat but refers to food, and is proved when God created Adam and Eve and gave them fruit that should be to them for “meat”:

Genesis 1:29 King James Version (KJV)
29 And God said, Behold, I have given you every herb bearing seed, which is upon the face of all the earth, and every tree, in the which is the fruit of a tree yielding seed; to you it shall be for meat.