In this regard Jains believe the same thing as Christians. You have to admire those Jains, striving to conquer their bodily desires. They'd never fit in Western society, where we all weigh 250 lbs. They do a better job at conquering their flesh and its desires than most Christians do.
Jainism shuns all sexuality with the exception of procreation within a marriage. This translates into no homosexual sex. Does that mean it specifically shuns homosexuality? No. It reacts to homosexuality the same way it would pre-marital sex. Marital sex is only acceptable due to the need for more people to practice Jainism, and not so much to promote one sexuality or the other. All sexuality is oppressed, it just so happens that homosexual sex could not be for procreation, married or not, and therefore not allowed at all.
Jainism is against too much sensual pleasure in general, not just homosexuality. There is nothing wrong with love, but Jainism purports that physical pleasures that go too are fall into the category of immorality. Sins of the flesh in Jainism are sins whether they are heterosexual, homosexual or transgendered. It's not a knock against homosexuality, it's a knock against human nature.
Jainism is not entirely clear about homosexuality, at least as far as I can find, but they are a traditionally very accepting, going so far as to walk with brooms ahead of them in order not kill small insects. Jains seem to be overall a very accepting religion, and this is a good thing to take into account.
No, I do not think their views on gay people are correct. It is not a sin for someone to be able to choose who they want to be romantically involved with. Who is one person to judge what another wants to do with their life, we all make our own choices.
No, I do not think that Jainism's take on homosexuality is not correct, because Jainism's position on homosexuality is ambivalent at best. It is okay to disagree with practicing homosexuality. Jainism appears to not want to take a side on homosexuality for not wanting to offend anyone. That is a bit weak. It is okay to disagree with someone's position but not condemn them as a person.