I got several square pieces, because I was able to get to a state where any other piece would fit into the remaining 1x1 hole, and so a square piece was the only thing that would block me.

No. For example, there are no flat part on your playing field, then you would get square.

Only if you can't use it to finish a line at that time, lol.

It depends on the algo. So not if it's optimizing for least placements to insert that would clear a row.

I layered S pieces horizontally across the bottom and then it gave me a long piece.