A level 8 character with 10 strength automatically succeeds at climbing a rope. Out-of-combat, a level 1 character (when taking 10) automatically succeeds at climbing the same rope.
I would argue that if there is any danger to climbing the rope (like falling damage once you're more than 10' above the ground) then you can no longer take 10.
I'm surprised that no one mentioned the opening phrase under Cooperation: "In some situations..." As DM, you decide what those situations are.
If the original check requires skill training in order to be allowed to make the check, I'd disallow any help. The level 20 fighter can't aid the wizard in trying to Detect Magic or the rogue in disarming the trap.