Sometimes When I pedal really hard, or start to skid, it feels as if something momentarily slips. Could this be my axle? So I tightened the axle nuts as much as possible. Is it bad to tighten the axle nuts too much? Was the axle slipping? Has anybody else had this problem?
If your axle would slip it would force the wheel against the frame and either stop you cold or make the wheel rub. It is not a good idea to exceed the torque rating on the axle or axle nuts, so yes, it is bad to tighten them too much. Your problem, assuming it is a fixie and not a single speed (freewheel), is that the rear cog is probably loose. Retighten the cog and the lockring and you should be fine.