Help, Don't know what is causing this

Sometimes after starting the car the engine revs on its own as if I'm pressing & letting up on the gas pedal. Usually if I press the gas pedal & rev the car quickly & release it will stop. Don't know if this is a fuel problem or computer?

Also I have started to expierence another weird problem. When I drive on a bumpy road the RPM's will surge 400 or 500 RPM's when I hit a bump. As if the car downshifts on its own & is grabing a lower gear. After a couple of seconds the RPM's decrease back to where the were before hitting the bump. I usually experience this when driving on the highway between 55mph-60mph. Some days almost any bump will cause this to occur. Other days it doesn't happen even if on the same road. Don't know if this is transmission related or something else? Please help.

how high does it rev? Like if it's cold when I start my car it will run at about 11-1200 rpm rather than the normal idle around 7-800. Pretty sure it's not a big deal, just needs to get warmed up.

On your second problem, I believe there are existing posts on that problem.