What side knob/pull for these small draws?

What do you mean by "side"? Perhaps you meant "size"?

As these look indeed small, I'd go with knobs rather than pulls.

I've used these knobs for my master bedroom entertainment center and was very happy with them. For white cabinets, I personally prefer ORB or Matte Black hardware for contrast, but do whatever looks good to you (I don't see an issue with mixing in a finish that's different from your brushed nickel faucet).

Do I mount them inside the recess area or above the recessed area?

I personally prefer the vertical center of the drawer (i.e. the recessed area). I believe this is generally the more popular choice too.

Thank you so much for the advice.