1. How do I create a custom form like this? I'd like to put it in my template in a module position
You'd need to develop it. We have no such thing. Best you could do is create fields for that search criteria then create a userlist for them.
2. Is this even possible? I need the form to search the correct List based on camp or trainer choice, then bring up the results based on sport and location (closest to their zip)
Yes, it's possible but you'd going to need to develop it. It's possible something like this is already available, but unlikely; you'll need to check Joomla.org extension directory. CB userlist searching has no radius zip searching so it can't do that without custom development.