I'm sorry if this question has been answered before.

but if you give clothes with a PE bonus to cait will she be able to pick licks more easy?

Also would PE bonuses be the the best Is luck involved?

Do legendary gear transfer to companions in general?

these are my questions thank you for your input

I do not know if SPECIAL modifiers affect companions or settlers at all.

I doubt any companions needs "charisma" or "luck" . You can easy test "strength". Fill your companions with stuffs until limit and then equip them with strength modifier. If they can keep more, it's working. Remember some TES game had a problem. Their inventory capacity may decrease even removing the stuffs from inventory. So we had to "reset" companion.

Cheers,

-Klevs

Increasing their SPECIAL stats does have an effect on their derived stats. So bumping Cait's strength with the Grognak Costume will boost her melee damage and carry weight. Some effects can't really be used by anyone other than the player, and since companion lockpicking/hacking is probably done with a script instead of a minigame I doubt their stats play into that. But who knows.