Saricane

Yes they may appear on the grass that spawn inside the fence. To prevent this, I manage to minimize the grass blocks. The water channel is under the fence (not inside), so the terra preta can touch the fence. And if, for some reason, I still have (because work in progress, or so ...) grass blocks, I put a flower on them, so the grass can't spawn. I even have a daily look on the fallow farmlands, because grass or horsetail sometimes spawns on them.
Sometimes they jump from the outside, with the help of a misplaced soil block, or chest. Better have a flat land outside the garden.
Last little advice : you should not have a shared wall with your house. The world is wide enough to put your gardens and your animals a dozen blocks away. In your case, it seems not to be the origin of the problem, but mobs have sometimes efficiently pathfinding that I underestimate. Moreover, it's difficult when you want to resize the house or the garden (don't forget a farmland is destroyed when moving, so terra preta must be carrefully placed).

No link between forest (or another specific kind of vegetation) and bears. Not linked either with wolves. Each kind of bear (5 types) spawns when min/max T° and min/max rain conditions are fulfilled. So roughly, it depends mainly on the latitude.
Keep in mind that bear stop spawning when light is 8+. So, putting lights around your base and most importantly around your animal enclosures will prevent them from spawning.