A1. Preposition Time: ~ time, ~ the end
a. On time: punctual, not late. (e.g. The 11.45 train left on time. (= it left at 11.45)). 
b. In time (for something/ to do something) = soon enough. (e.g. Will you be home in time for dinner? (= soon enough for dinner)). Can say just in time (= almost too late) (e.g. We got to the station just in time for our train.) The opposite of in time is too late. (e.g. I got home too late to see the game on television.)
c. At the end (of something) = at the time when something ends (e.g. I'm going away at the end of January.) 
d. In the end = finally (e.g. We had a lot of problems with our car. We sold it in the end. (= finally we sold it)) 

back means backwards to a place, a person etc. (= go back, come back, take something back etc.) (e.g. Can you please call me back?)
back away means to move in a direction opposite where one is facing, keeping some (or most) of your attention on the thing in front being avoided.
back up means to stop or to wait in a long line because there are too many of them (e.g. My car backed up for miles after the accident.)
back up someone/ something means to provide support or help to someone or something (e.g. My boss always backs up my arguments with facts.)
back something up means reverse, or to prove that something is true, or to make an extra copy of information (e.g. You should always have to have backup plans for any situation.)