In this manner, how long can momos be stored?
I usually freeze them in medium freezer bags (about 8-9 pieces/bag) and date them. It's easier to pack them in small batches and thaw according to need. Just add the frozen momos to boiling water for 5 minutes and they are ready to use. I usually freeze them for 30 days (especially if they have meat as filling).
Beside above, can I make dumplings ahead of time?
You can make it days ahead and refrigerate, or freeze huge quantities. The dumplings whip up so quickly, and can be refrigerated for up to a day or frozen for months. You might consider making a double batch and freezing some to have on hand.
If it makes any difference, I used store bought Shanghai dumpling wrappers. Freeze anything you're not going to use the same day you make them (as people have said, single layer on a cookie sheet or plate, with flour or parchment paper to keep them sticking to the plate). Shake them off into a ziploc bag.