If I'm not mistaken, there's one natural gay character (trap) plus there are plans for making every heroine have a reverse-gender option (some animated scenes should already be in the gallery).
It might have some issues with the beta exclusive content but otherwise I think it should be fine.
Almost none, there is 9 animations if i'm not mistaken (from 122 total), gay content is not the main focus of the game.
Is Kobold excluded? Despite the fact that she's grouped with you at the beginning, but I do know that she has her own route too. And wouldn't that lock you out of the dragon route? Given their issue? Though guess it's fair that she is happy-timable due to her grouping with you at the beginning. But the route pends on the questions answered, dragon/dog/ etc etc.
No, you can only do a single route per new game or new game +, as entering a route will lock you out of all the other routes, Kobold princess included. The current routes available are Kobold, Slime, Skeleton, Cat, Dog, Wyvern, Dragon 1, and 2. Out of those you can happy time Kobold, Skeleton, Cat, and Slime without going into their routes. Dog, Wyvern, Dragon 1, and 2 I believe cannot be happy timed outside of their routes.
That would be nice but I believe they are currently working on Ghost princesses route.
Officialy, no and most likely wont ever happen because of patreon. However like you mentioned there is the unofficial patch but I dont know how up to date it is or if it will work for the newer builds. https://f95zone.to/threads/princess-conquest-v0-17-14-beta-towerfag.602/post-5072557
