Welcome to FT.

Signing up for a frequent flyer (FF) program has nothing to do with earning points or spending on that card. You should always sign up for FF programs since they are free (most if not all?). It will earn you status in their program if you fly enough with them.

Depending on the airline, some may not give you points (or bonus points) unless you make a purchase directly on their website. But either way, you should earn Chase Ultimate Rewards (UR) points as long as the merchant/airline is listed in the "travel" category. Also if you book it through the Chase UR Mall, you should get some additional point(s) there too (via Expedia, Travelocity, etc.) but you might be better off using some of the cashback websites.