Women, what do you think when a guy facebook friends you in this way? What should I do?

Sounds like an open door to get to know each other. See if you can set up some times for her league and your league to get together, hang out, talk sports, etc. Honestly I'd be weirded out by somebody who friends me, asks me a few questions about our similar interests, then starts hitting on me. Just get to know her a little first, hang out a little, etc.