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Brian -- I've got a Sheng En F2 as well, and I like it quite a bit (I don't have a lot of other cubes, just a Haiyan's Memory Cube [only had it for a week] and a Ghosthand II) but, I had the same problem. The caps would pop off here and there. Seeing that I only really need to take the caps off the center cubies, I decided that when they would pop off I'd super glue them back into place. I used super glue with the precision tip. However, if you decide to go that route -- I recommend putting just one drop, and do it inside the cubie, not on the cap. Cause some will want to squeeze out. It's not a big deal if that happens, just use an exacto and then wet sand it. Now that I've done that (and re-stickered it, cause the stickers were terrible), my F2 is my main cube over the Ghosthand (however the haiyan's is quickly becoming my fav).
Don't bother with learning OLLs for quite some time. I'm still using 2-look and there's a vid Erik Akkersdijk put up of him doing beginner's LBL method with 4-look last layer and he had a sub-20 average. If you're still pulling out your bottom layer cubies then you need to work on F2L a lot. Efficient F2L, Cross and 4LLL can take you pretty far but if you're doing 3LLL you can easily sub-30 it and even sub-20 with just that. You don't really need to learn more. Just practice what you know. If you're that close to finishing full PLL then finish that up but after that focus on F2L. You should be able to pair up you corners and edges in the top layer and then insert them together without having to pull out the white corner for most cases. If you haven't watched badmephisto's F2L tutorials I highly recommend them. More than anything else. I'll get the links to his vids.
Part One
http://www.youtube.com/watch?v=k-xbcAMfWwM
Part Two
http://www.youtube.com/watch?v=4GxLM_dZqg4
Tips for Practicing F2L
http://www.youtube.com/watch?v=pnkSZZ6OoQ4
His Thought Process while doing F2L
http://www.youtube.com/watch?v=pzkHrz8x2eo
Those are all you need for awhile