Filemaker can do all you describe, but the key question is: "can you do it with filemaker" Filemaker comes with a set of template files and the tools for building your own solution. You won't find what you describe ready and waiting to be used. Instead, you'll have to either create your own solution from scratch or adapt a template file to your needs. The contact manager sounds like it'll come pretty close, but probably can't send out the renewal emails you describe without further modification.
You might want to download the free 30 day trial copy and see if you can make it work for you.
Thanks Phil. I knew it wouldn't do it "right out of the box". I am completely ready and willing to put some time in and "get my hands dirty." Just wanted a couple of opinions from longtime users, as to what they thought. If FileMaker is the right tool for the job or was I barking up the wrong tree. Thanks again.