Druid charmed pets
 

Can they be given weapons and will it effect their dps and proc?

Both no drop and droppable?

You can give them droppable weapons and they will affect dps and can proc. Pets dont equip no-drop items.

Have a mage summon you some rune swords and a muzzle for haste

AFAIK this is no longer true and nonhumanoids (= all druid charms) will not wield weapons. For sure this is true in Fear with the gorillas.