It would only make sense to buy your lifts off mountain if you were getting a discount. I don't know of any place off the resort that is going to sell you a ticket to Keystone cheaper than they are. There was a five pack discount lift ticket that might have been cheaper but I don't think it is available any more.
As for renting you equipment at the resort or away, that is basically up to you as far as what you are tyring to achieve. Renting at the mountain will always be a bit more expensive than off site. I assume you are flying into Denver and driving to Keystone? There is a Breeze ski rental right after Idaho Springs that will be cheaper than renting on the mountain. What you will give up is the ability to take your skis back and switch them out for something else, which is a plus if your rental shop is at the base. If you want something really specific you will have more choices at the mountain. A shop your rent from off site will have a great selection, but you won't have 5 different store within walking distance to choose from as you will from the resort.
In regard to your buddy who has never skied before and should he take a lesson, I guess that depends on how experienced the rest of the group is and how you want to spend your time. Not from a stand point of being able to teach him, but from a stand point of do you want to be held back by him for your entire stay? If you guys are skiing blues and blacks all day now, you will either end up losing your new guy during the day or end up hating him. If that is the case stick him in some lessons each morning so you guys can enjoy yourselves and meet up with him for lunch and then ski with him. If you all are pretty much beginners then the above doesn't really matter as much, and you would all benefit from a lesson.