How important is item sharing?
Pretty important. Especially when you both have different weapons and need ammo. I gave Sheva the pistol+ammo and grenades. She never uses grenades, though. Even when she's out of ammo. So I'll have to rob her from a grenade when I need one.
I personally don't give Sheva any health restoring items. I'm afraid she won't use them wisely.
But when she collects any ammo that you need, she'll automatically handle them over to you. That's pretty handy.
Sheva is nothing more than a walking item storage medium to me, who helps me from time to time. I don't feel any connection with her.