Each state has its own laws about the eviction process and tenants' right. If go to Eviction you can research the laws for your state.
Yes they can but pregnant has nothing to do with it.
If you live in a big city with rent control laws you will most likely be able to stay, your local library should have a booklet om tenant's rights. You can also call your county attorney and ask him about your rights.
A landlord can evict you even when you are pregnant. A landlord have to give the tenant 30days notice for eviction.
Yes, he can pregnancy does not stop you from paying rent.