I believe that CPT-onomies may do what you’re looking for. The plugin allows you to use a post type as a taxonomy, so you would set up Team Members as a post type and include their post information, but then be able to use each post as a custom taxonomy as well.
As for the other issue, parent/child post types is another plugin issue. I haven’t tried Posts 2 Posts by Scribu, though I’ve heard good things about it, but I have tried Types. Both allow you to create relationships between post types. The example provided for Types is to have three post types: Cars, People, and Rental Agreements and use Rental Agreements to link Cars and People. My personal example was to make Signatures a child type of Posts.