[Heavydrop]

Research is level capped.
I don't know the specifics but yes, the more you level the higher the
skill cap goes.
What I typically do, unless you really need to research something, is NOT
skill it right away at 16 because, as you've noted, it instantly bumps your
skill up to 16. If you can, hold off on it and when you do train in it you'll get
those extra skill levels for free (train at 20, get skill of 20, etc)
Too late for you to do that now but something to keep in mind.
I don't know why it would be showing a red number