It depends on the block, for me, but lately, I haven't been pressing much. For a 9 patch, I sew 3 sets of long strips together and cut to my square width from the strip then sew three strips to get the 9P, so yes, I'll press before cutting the strips.
But I don't press each seam as I go unless I have to, like if I'm sewing over a seam, I usually will, though I've been finding that I don't really need to if I position and pin it properly.
I press my seams open. It is really a matter of preference. I prefer them open.