Thank you for coming here and posting this. These are exactly the kind of lessons that people learn as they dive, and you've drawn some very good conclusions.
One of the things I see people jettison almost immediately after their classes is a buddy check. A good buddy check will pick up a lot of problems with equipment before you get in the water -- and you're totally right; if you think something is not quite as it should be with your gear, don't experiment with it in the water!
With respect to your problem with popping up during your 15 foot stop, I wonder if you weren't a fair bit overweighted. We put the amount of lead you are describing on our OW students, who are wearing 7 mil suits with 7 mill core warmers; in a 5 mil suit, I use eight pounds in fresh water, which would be about 11 pounds in salt. Of course, if you are a very large person, you could need more. But if you are overweighted, that means you have a lot of gas in your BC, and when you are that shallow, the proportional pressure changes are huge. Very small deviations off stop depth are going to make big changes in your buoyancy, at that point. Next time you go, see if you can get an opportunity to do a formal weight check. It may help.