Well, of course you don't throw it randomly into a sentence. We understand the sentence as "I can't give up / on you." Same goes for "sneak up / on you" and "creep up / on you". However, you use "wait up / for you" and "hold you up" (ie. can mean either "support" or "delay" you). You'll have to learn these as you encounter them.

Depends. With "wait" then "on" is not used" Example: "Wait for me", "wait for him". The interjection "wait up" also does not use "on". Same with "hold up" because it means two things; one; to wait and two; to raise. (as in raising a object. The song "Raise your Glass", not as in like "raise one's pay".) Both meanings of "hold up" do not use "on" except the second which then it uses "onto". These are few irregularities, but most other phrases can use "up on".