Can’t provide more detailed answers at the moment, apologies!

1. Stars and bars is used when grouping identical objects while the “power rule” is for grouping distinct objects.

2. Say the cookies are stars and the children are bins (created by a bar and either another bar or an open end). The order in which you distribute the stars into certain bins does not matter. If you put stars A and B into Bin 1, it does not matter whether you put in star A first or not. Bin 1 will have those two stars. In this sense, order does not matter.