is grabbing someone assault? ?

Nope................

Yes, that can be assault.

It depends, if you are in a situation where the touching is socially acceptable like a crowded bus that stops suddenly then consent is implied.

Maybe.........................

Yes in today's world it is 20 or thirty years of more it wasnt.
It could sexual assault just putting your arm around a woman 

Yes it is.  Even if you are trying to help them.   Like grabbing the jacket of someone who is about to step off the street corner in front of a bus.   If they fall down and break their arm, you are responsible even though you might have saved their life.