This is all very possible. I have several PayPal and eWay solutions but it is years since I looked at Authorize.net. They all pretty much work the same way though and the API documententation is pretty good these days. I could manage the PHP interface and probably a number of others on the list could too.
I suggest you start by googling keywords "FileMaker" and "Authorize.net". I am sure I saw a demo download somewhere...
- Lyndsay (alias Cato)