Recently, When the gear is in reverse, I can feel a terrible vibration from the Engine,

is this normal? I got 40% oil life left.

It (the vibration) just feels like friend's 90' accord...

 

Not normal imho. Sounds like a broken motor mount-trip to dealer-warranty repair.

 

My car (and others, I think) does not idle smoothly for the first few seconds, but after that, it runs like butter.

I would take it to the dealer.

The oil life has nothing to do with it (unless, of course, you ran it out of oil - which I doubt).