How to make characters overlap each other but when they do they push away from each other

What exactly shall overlap and when should they start to be pushed away?

For overlaps which take too long, you could start a timer in the “Begin Overlap” event which is then increased by event tick until the “End Overlap” event is called. If the timer takes too long, you could temporarily create a collision component which blocks the other character and pushes it out of reach.