Do the various legendary and stat effects apply when the gear is equipped by companions? Do they, for example, actually benefit from +1 Perception or "Reflects 10% of melee damage back on the attacker" equipment?

I don't see why it wouldn't...legendary effects on weapons work when companions use them..

It would be hard to tell tho with armor effects on companions I'd think..I'm usually not paying much attention to my companions during a fire fight..

+1 to agility or perception wouldn't do anything as NPCs don't use VATS. But the other Legendary bonuses would apply I think.