1) Don't. Wire up the outlet for four wires hot,hot,neutral,ground and change the pigtail on the stove to a four prong to match the outlet.

As long as you have the correct wiring you might as well do this correctly all the way.

I was not sure I could change the stove 3-wire config to a 4-wire. Than makes outlet and breaker box easy, however, I am not sure what to do with the white neutral and ground on the stove.

I don't know all the stoves but basically there will be a terminal block for 2 hots and the neutral. There should be a jumper from the chassis to the neutral connection, remove this and fasten the ground to the chassis.