I live in So. Ca. On vacation in China everyone had finches outside. Can I keep Finch's outside in So. Ca.?

Yes, you can. As long as the birds can get out of the direct sunlight if it wants. I have a friend in So. Indiana. That put his out under a carport every spring. He would tie the door open and they would raise babies like crazy. He didn't have to feed them much as they foraged around his area. It is built up around him so I don't think it would work so well now.