Yes...yes...and... yes(to small rats)! I had the same question the first time I can babys, and two are still with meBy the time the baby rat is ready to eat and drink after they leave their mothers, I find mine climbing upside down on the Hardware cloth to get food and water.
You can start with older rats, but I wouldn't. For all you know the females could be retired breeders people sell to petstores. If you want you can start off with a few adults, and just make sure that you hold back all the female babys.