I can't seem to find how a hero can give an item to another hero. Any idea? Thx.

On the map have two heroes occupy the same Province. Then an option will come up in the interface about exchanging items between the two heroes. You can also trade troops this way as well.

Unlike visiting a neutral store to repair items, this does not use up their turn.

The icon Rezca describes is the rightmost one, next to the hire units/garrison one.

Thanks guys, found it!