Pre-making Gnocchi

Most certainly you can. In fact, you're describing what restaurants do as a matter of routine. Before storing in the refrigerator, be sure to toss it in some olive oil to prevent it from sticking together. Just enough to gently coat it is fine.

Yes, and whenever I make gnocchi, I make at least a double batch, and toss them with a little oil, then cool the extras and freeze them in heavy duty ziploc bags in the freezer. So handy to pull out and either microwave, from frozen, or heat in a frying pan with a little butter and whatever else tastes good . . . onions, bacon, sundried tomatoes, pesto ...mmmm.

Absolutely. Par-cook it, drain, toss it with some oil, cool in a single layer and refrigerate. Take it out of the fridge 30 minutes or so before sautéing.