The yellow is more of a leather protector. So I would eliminate any unsmooth areas. Otherwise don't worry about it. Reapply in a decade if the leather gets dry. Use your hand (and the oil on it) to treat the strop. You can wipe your forehead in the morning and then rub the strop if you have dry skin without much oil.

The razor should not bounce or bound on a strop. If it does eliminate the nick.

You want a wider strop, perhaps, not a thicker strop. It sounds like you need more practice before buying a new one though. There are some good starter strops.

If you mean a paddle strop you won't screw up the blade. Who told you that? Stropping with a paddle is a little different, but not much. I would stick with a hanging strop. You'll learn soon enough and the extra length is a bit of a help.