Correct me if I'm wrong Moe, but here are some of them. I'm slightly confused on 2, 3 and 4.
Your confusion is well warranted, as that site does a terrible job of explaining the paradoxes. In fact, they way they are presented there, they aren't paradoxes at all!
So, just to be clear: a paradox is a kind of situation that results in a logical contradiction. None of the paradoxes on that Website are clear contradictions. I'll take them in turn.
1) "If you have transcended to Heaven while your spouse transcends to Hell, then can you fully experience ultimate joy and happiness?"
This is the most common paradox, but it only make sense when you include that God's will is determinate and unerring. If there would even be just a smidge more happiness in heaven with a loved one, then it would seem to guarantee entry into heaven by that loved one. But there are ways around this, here's a better way of putting the paradox.
John loves Sue but Joe hates her. John and Joe die and go to heaven. Sue's presence would make heaven that much sweeter for John, but would make it miserable for Joe. Where does Sue go?
2)"Our physical bodies bring us astounding agony in life. What substitute does Heaven offer for one's physical form?"
I can't make sense of this one, either. It's just a question, not a paradox.
3) "As defined by religion, our lives our filled with seemingly unavoidable sins. Does Heaven deprive us of our human minds in order to avoid sinful thinking?"
Simply put: sinning makes us happy. The things we're really not supposed to do are often the things we derive a great amount of pleasure in. It seems like eliminating these desires would make you not really... 'you'. So if 'you' go to heaven, then you don't
4) "The declaration of Heaven as a place for those who are saved means that there truly is a set of objective moral values. The problem with this perspective is that every religion basically has its own set of objective morals. Which one is correct?"
This is the idea of mutually assured destruction. Lets look at it from a Christian standpoint. Catholics think that everyone who hasn't received communion is going to hell. Baptists believe that anyone who isn't baptised as an adult is going to hell. Pretty much every Christian thinks, in some sense or other, that everyone else is going to hell but them. (Not literally, of course, but enough to get the paradox going).
Since all these groups claim to have the divine word of God and its correct interpretation, it seems like God messed up, which isn't possible.
I'd just like to point out that these are only paradoxes under certain conditions. They're really not 'true' paradoxes. But I think they cast reasonable doubt on the idea of heaven.