Willie,
Yes, you can apply with a buddy. They call them party applications. Either you both draw, or neither.
Forget unit 52. New Mexico has a unique method of pricing their hunts. If a large number of nonresidents apply for a specific hunt one year, the next year they classify that hunt as HD and jack the price up. Thus hunters swing from these marginal quality units to other marginal units. Some hunts ping pong every year. It looks like NM split the unit 52 archery hunt. The second is more near the peak rut but it's only 7 days! That is crazy for an archery hunt. I don't think I've ever seen one so short. Stay away from both those hunts. You'd be much better off applying for 44/45 if you want to backpack, and 49 if you want to hunt from camp. Both are regular hunts. By the way, in NM you have a very good chance of drawing your 2nd or 3rd choice hunts. You should pick a great hunt for #1, then maybe another slammer hunt, then either 49 or 44/45 as your 3rd choice. Pick Valle Vidal as your first choice. Maybe 15/16 as a 2nd choice.