Things I Don't Understand

I keep thinking that I'm beginning to get things figured out, and then God shows me more scripture. I was reading the beattitudes this morning and saw some things I just don't get. Then I read 1 Corinthians 5 and my entire Christian attitude dynamic was thrown for a loop.

Matthew 5:8 NASB: "Blessed are the pure in heart, for they shall see God."

They shall see God... with their eyes? They will go to heaven and be in His presence? What does He mean when He says "they shall see God," anyway?

Matthew 5:3,10 NASB: "Blessed are the poor in spirit, for theirs is the kingdom of heaven."
"Blessed are those who have been persecuted for the sake of righteousness, for theirs is the kingdom of heaven."

What is the Kingdom of Heaven? Is it the presence of God? Is it "heaven" as most Christians tend to think of it? This white place that we "go" to worship God after we die? Thus far in Matthew, Jesus and John have each said "Repent, for the Kingdom of Heaven is near." So what is the Kingdom of Heaven?

1 Corinthians 5 ESV: ¹It is actually reported that there is sexual immorality among you, and of a kind that is not tolerated even among pagans, for a man has his father’s wife. ²And you are arrogant! Ought you not rather to mourn? Let him who has done this be removed from among you.
³For though absent in body, I am present in spirit; and as if present, I have already pronounced judgment on the one who did such a thing. ⁴When you are assembled in the name of the Lord Jesus and my spirit is present, with the power of our Lord Jesus, ⁵you are to deliver this man to Satan for the destruction of the flesh, so that his spirit may be saved in the day of the Lord.
⁶ Your boasting is not good. Do you not know that a little leaven leavens the whole lump? ⁷Cleanse out the old leaven that you may be a new lump, as you really are unleavened. For Christ, our Passover lamb, has been sacrificed. ⁸Let us therefore celebrate the festival, not with the old leaven, the leaven of malice and evil, but with the unleavened bread of sincerity and truth.
⁹I wrote to you in my letter not to associate with sexually immoral people— ¹⁰ not at all meaning the sexually immoral of this world, or the greedy and swindlers, or idolaters, since then you would need to go out of the world. ¹¹But now I am writing to you not to associate with anyone who bears the name of brother if he is guilty of sexual immorality or greed, or is an idolater, reviler, drunkard, or swindler—not even to eat with such a one. ¹²For what have I to do with judging outsiders? Is it not those inside the church whom you are to judge? ¹³God judges those outside. "Purge the evil person from among you."

Romans 14 ESV: ¹As for the one who is weak in faith, welcome him, but not to quarrel over opinions. ² One person believes he may eat anything, while the weak person eats only vegetables. ³Let not the one who eats despise the one who abstains, and let not the one who abstains pass judgment on the one who eats, for God has welcomed him. ⁴ Who are you to pass judgment on the servant of another? It is before his own master that he stands or falls. And he will be upheld, for the Lord is able to make him stand.
⁵ One person esteems one day as better than another, while another esteems all days alike. Each one should be fully convinced in his own mind. ⁶The one who observes the day, observes it in honor of the Lord. The one who eats, eats in honor of the Lord, since he gives thanks to God, while the one who abstains, abstains in honor of the Lord and gives thanks to God. ⁷For none of us lives to himself, and none of us dies to himself. ⁸For if we live, we live to the Lord, and if we die, we die to the Lord. So then, whether we live or whether we die, we are the Lord’s. ⁹For to this end Christ died and lived again, that he might be Lord both of the dead and of the living.
¹⁰Why do you pass judgment on your brother? Or you, why do you despise your brother? For we will all stand before the judgment seat of God; ¹¹for it is written,
"As I live, says the Lord, every knee shall bow to me,
and every tongue shall confess to God."
¹²So then each of us will give an account of himself to God.
¹³ Therefore let us not pass judgment on one another any longer, but rather decide never to put a stumbling block or hindrance in the way of a brother. ¹⁴I know and am persuaded in the Lord Jesus that nothing is unclean in itself, but it is unclean for anyone who thinks it unclean. ¹⁵For if your brother is grieved by what you eat, you are no longer walking in love. By what you eat, do not destroy the one for whom Christ died. ¹⁶ So do not let what you regard as good be spoken of as evil. ¹⁷ For the kingdom of God is not a matter of eating and drinking but of righteousness and peace and joy in the Holy Spirit. ¹⁸Whoever thus serves Christ is acceptable to God and approved by men. ¹⁹So then let us pursue what makes for peace and for mutual upbuilding.
²⁰ Do not, for the sake of food, destroy the work of God. Everything is indeed clean, but it is wrong for anyone to make another stumble by what he eats. ²¹ It is good not to eat meat or drink wine or do anything that causes your brother to stumble. ²²The faith that you have, keep between yourself and God. Blessed is the one who has no reason to pass judgment on himself for what he approves. ²³But whoever has doubts is condemned if he eats, because the eating is not from faith. For whatever does not proceed from faith is sin.

Looking at Romans 14 again I see that it's a different context -- eating unclean foods, rather than sinning sexually -- but I'm still a little confused. While it is obvious to me that sinning sexually is unacceptable -- Paul frequently condemns sexual sin in his letters, and Jesus told the adulterous woman to "sin no more" -- I am not sure that I understand how it is that some of the old law, like circumcision and unclean foods, are no longer necessary, but other parts, like sexual purity, are still necessary.

I understand that holiness is a must for Christians. Does 1 Corinthians 5 change how I react to my friend who claims to be a Christian but is living with her boyfriend? What about someone who claims to be a Christian and says she is a lesbian as well? I know I'm supposed to love them, but Paul seems to be saying that love towards a sinning Christian is not always "nice." He tells the Corinthian church to exile a man for his sin! I see that it is so that "his spirit may be saved in the day of the Lord," but it seems so harsh to me. Am I making it more complex than it needs to be because I'm reluctant to accept a difficult teaching?

Does his council even apply to me, since the friend who is living with her boyfriend is not part of my church community? The Corinthian church was made up of all the Christians in Corinth. Does this mean that my "church" is made up of all the Christians in my logistical community?

I'm not looking for an answer from human reason, but from scripture. I am sure that there is an answer and that I will find it eventually. I apologize for asking so many questions without offering many answers.