FileMaker can be set up to do everything you describe, but can YOU do it with FileMaker? That's not a question we can answer as we have no idea how much prior knowledge and experience with database design you can bring to such a project. The data model you'd need to set this up is unlikely to be something a person new to database design can easily set up by themselves and it's unlikely you can find a ready made solution for this--but you never know until you do some web searching. Be prepared to invest significant time in learning how databases should be designed and in how to use FileMaker.
FileMaker 11 is available as a free 30 day trial that you can download, so you may want to download it and play around with it a bit to see if you can figure it out.