I flew a cat to the USA with British Airways and she was very well looked after. They fed and watered her and she was well looked after. I had to get a vet to certify she was healthy before she could fly.
The airline was very strict about the type of cat carrier that would be acceptable. The internal US flight required a different cat carrier which meant I had to change her over at Houston, where she briefly escaped and had her food confiscated as it was a health hazard. She travelled with me in the plane from Houston and she coped very well with what was a difficult day (for us both)
You can find all the information you need on the airlines web sites.