When I stand up to sprint in a race (or rather, attempt to, I'm not good at it yet), my front wheel often bounces off the ground and twists to the side. Needless to say, this is rather disconcerting and probably inefficient as well. Anyone know how to stop this?

I've also noticed that my steering was dangerously unsteady today. I could barely use my downtube shifters without wobbling to the sides.

Could either of these things have to do with using a 20 mm front tire and a 23 mm rear tire? I got them for free, and am using them just to try them out. Previously I had two 25 mm tires. I'm 6'1" and weigh about 165 pounds.