Do some research on this. Should be some youtube videos about extending a circuit and pulling wire. It sounds like you have never done this type of thing by your post.
The 12V wiring for your ceiling light will be a run of two wires, 14 ga. will be adequate. I disagree that this will be an easy task to pull wire through the ceiling and down into a wall cavity. This will be especially true through an outer wall filled with foam or in the ceiling cavity through the joists. It will be much easier to establish a run under raceway to a surface mounted switch. As your child grows, the whole business could be removed.
The 120V receptacle location above the countertop is a good idea. I would extend the circuit from the existing GFCI. Any receptacle within a few feet of a water source should have GFCI protection. You could, of course, extend the circuit and add in another GFCI. That becomes problematic using a shallow old work box, the best choice for your new receptacle. You will need to pull wire from the existing GFCI to the new location, I would use 14 ga. if you have a 15 amp circuit breaker powering the GFCI, 12 ga. if you have a 20 amp. Cut an opening into the wall behind the countertop big enough for the old work box, leaving enough room if you have foam behind the paneling for the two attachment arms to swing inside the cavity. Use a metal snake or fiberglass rod to pull the wire into the new location (a coathanger will sometimes also work for this).
If you haven't done this type of thing, previously, I would enlist help from a relative or friend. Done incorrectly, there can be safety issues.
I wouldn't mess with the water pump switch. It is too problematic for any perceived inconvenience. You only touch it twice, usually, for a given camping setup.