Welcome to the world of fixed gear riding. Once I got my first one set up my geared bikes has seen almost no road or trail usage. I do cross train on mountain bike trails geared with full suspension though. Riding fixed sure has improved my spin.
I never had much of a problem from day one, but we all get reminded by the pedals occasionally. I use platform pedals so it's not hard to get going. My knees are old and
my gearing is as high as 52/16 so I use my brake(s) to stop with.
Some fixie riders hop off their bikes in motion and grab it by the saddle as it goes underneath them. I just come to a stop, put my left leg down, then swing my right leg over to dismount.
I go as fast, if not faster riding fixed. It's actually easier to go fast once you find a good cadence.