Parchment paper?

Yes

Yes, buns in Chinese restaurants and frozen ones usually have a bit of paper under them to prevent them from sticking to the steamer. When you steam other Chinese goodies that don't have paper under them in a steamer (I like the stackable bamboo ones), you can put a leaf of lettuce (or a paper towel in a pinch) under them so they don't stick

Yes, cut out small squares or the dough is going to stick to the steamer.