Chainstay is fine. Frame is fine for a fixie conversion.

Oxalic acid, found in Savogran Wood Bleach, sold at Home Depot, will get rid of that rust. You'll need a kiddie pool or large enough tub to soak the whole frame in a solution of the oxalic acid. Removes rust from chrome parts, too. When the rust is gone, rinse very, very well then dry the frame with paper towels then wipe down with an alcohol soaked towel to make sure it's really dry. Prime the frame asap to prevent flash rusting.

The best part about the oxalic acid solution is that it will remove rust from inside the tubing. There's a spray called Framesaver that you use to coat the inside of the tubes to prevent rusting there.