Beat the cap kingdom only crouch walking, Sideflips, frontfliips, backflips and Cap throws

I don't understand what you mean by this. Are you allowed to do normal jumps, capture things (frog), etc.? And what is the point/what sets it apart from any% cap kingdom?

you can only walk by crouching i think. that explains both your questions

analogously to the ABC (A-button challenge) in SM64... :)