would a larger rock dropped into a large pan of water make a larger wave than a smaller rock, and which would travel faster?

Answer 1

The larger rock would make a larger wave, but it would travel at the same speed, unless it were of very large (e.g. asteroid) size. In that case, an enormous and fast tsunami would form.

There are phenomena called solitons in water waves. Tsumanis are an examnple. They travel much faster than low amplitude waves.