You also asked about the propulsion of a kick. I find I use almost no kick at all, nor do I need one. When I do choose to add a 2-beat kick, I find I tend to kick too big and end up slower rather than faster. You might try going without the kick and just trying to focus on floating your feet high (sometimes I get the sensation of swimming downhill, which is when I know my feet have popped up and given me better balance).
Many swimmers turn in faster times with a pull buoy than when they are kicking. I'd try to duplicate that balance and ease rather than expending my energy in kicking.