Some DNA methylation is "permanent", e.g. the methylation that "turns off" teeth in birds, and some of it occurs during the life of the critter. For the most part it's not "inherited".
Not necessarily. While I believe that the behavior aspects of homosexuality are learned, a genetic component would not necessarily be reproductively futile, especially if one considers that its practical effects on males and females may be different.
For example, a gene which causes someone of either sex to be unusually-strongly attracted to males would likely not improve the reproductive success rate of men inheriting it, but could improve the reproductive success rate of women. If the latter effect was at least as strong as the former, the gene would continue to be spread to men and women as a consequence of the women who inherited it.
Further, there can be evolutionary value to genes which behave randomly. If some family groups had a gene which causes a random 5% of males to refrain from having children themselves but assist their relatives, such a gene might benefit such groups as a whole even if it quashed the reproductive success rate of the 5%.
I see no reason to believe that there isn't some genetic component to homsexuality, but just because something is influenced by genetics does not mean it should be given automatic license. I would not be at all surprised if there are genetic components to pedophilia, kleptomania, pyromania, alcoholism, and many other pathological behaviors, but that doesn't mean that people engaged in such things should be given free reign. People need to learn to behave acceptably even if they'd be genetically predisposed to do otherwise.