I love my cat dearly, but I wouldn't trust her around my 2 1/2 month old chicks; I'm always there to watch her. I don't care if she, or the neighbour's cat go into the coop when there are only adults though (standard breeds). Personally, I would't trust a cat around bantams, especially Seramas...
I'm glad you had the space to move your birds last year. Although chickens will catch and eat mice, the rats are too big for them. A cat won't be a problem for adult chickens, but both it and the rats are a problem for chicks (if you raise chicks). I have only ever had one rat, and I let it stay...