Yes to all questions. FileMaker can do this. What we can't tell you is how successful you can do it with FileMaker. Given your programming experience, you should be able to get up to speed in FileMaker fairly successfully, provided you keep in mind that FileMaker does not use SQL to query a table. You'll have to learn how it's done in FilMaker.
There's a demo version you can download and use for 30 days to get a feel for how FileMaker works.
You can click the downloads link at the top of this screen and use it to find a PDF on how to design for FileMaker Go--which would be a good thing to read before you buy any software.
Thanks PhilModJunk. I'll check out the Trial version and the PDF