1. Funtime Foxy's gender is also yes, since in Sister Location they're refered to as "her"(Said by hand-unit with the line of: Unlike Ballora, Funtime Foxy is motion activated, for this reason it is important to keep the room dark as to not accidentally activate her.). In UCN they were given the voice.
2. LolBit wouldn't've been even considered during FNAF 2, but it could've been a thing instead of getting Shadow Bonnie, so there might've been a "Mangle Lolbit" at some stage, but the idea would've properly occored during Sister Location
3, 4, 5 and 6: Mangle and FunTime Foxy do have those differences, but that doesn't mean they CAN be the same character, but a DIFFERENT model, which we've seen a bunch of times which each FNAF game. It's the same character, but a different model. (eg: Toy Freddy is still Freddy, just a different model type.)
In the books, there is such this as "Funtime Mangle", which is exactly what is expected. Funtime Mangle. I'm not sure WHICH book they come from, I just know they exist in the books.
So in conclusion, depending on the side you're on, Mangle is Funtime Foxy, but a different model, or they are they're own seperate characters entierly