Can I equip my survivors in Fallout 4

You can talk to them and trade them items via the trade conversation topic.

You can force them to equip something by hovering over the item, and press (T on PC, Triangle on PS4, and Y on Xbox) to have them equip it.

edit: PS4 button credit djsmiley2k

edit2: XB button credit VanBuzzKill

Mainly this is the main time spending as the building the settlement - to equip your settlers with weapons and armor. And every person you interact as the settler or companion could wear armor and hold the weapon you can give to. Please do not forget ammo. Meanwhile for settlers just several pieces means unlimited ammo during the attack.
There is one more idea - to equip better your guards with armor and weapon which means settlers assigned with guard posts. But I want to say that in real game guard posts do not play the important role outside of the defence score - the first settlers run to fight usually are farmers in my settlements.

About skills - there is no information or confirmations about any skills between the settlers - so they will use any weapon without any additional advantages. About companions the situation is other - they grow will levels, they have perks so for MacCready it is Killshot and it means that more clever to equip him with the guns.