Questions - Hero Equipment

I have been confused about this since NF came out, and I wouldn't mind if someone could help me.

1. If you put runes on your heroes and change their armour (eg - basic armour to primeval), do the runes stay on?

2. Lets say, if I give a customized axe from my warrior to my monk's koss, will the dmg boost still work? or must the weapon be from the char the hero is assigned to?

3. How do I get rid of my heroes starter weapons? I cant sell them or drop them.

1.yes
2.you cant equip it on your monk's heroes, since its customized for your warrior.
3.delete them, us the bin in your inventory.