NO, the school cost is not put into play when awarding scholarships.
Intended major and Whole Candidate Score (WCS) is the basis regarding how scholarships are awarded. Understand that it is done on a national level, so you will be competing against everyone, not just the candidate who wants to go to your school choice.
AFROTC does not care if University A has 100% on scholarship while College B has 0%.
I am a little confused on the 2nd question, because that is where it gets tricky. For example, GMU does not have an AFROTC det., the cadets must travel to UMDCP for ROTC, however you can be on scholarship at GMU. This is commonly referred to x-town ROTC.
X-town is doable, but you really need to think about it when selecting colleges. UMDCP has cadets coming from WV due to the fact that it is the closest host unit. It is even a bigger deal in metropolitan areas due to traffic. In DC area (MD/NoVA) it can take 45 minutes to an hour to travel 20 miles at 6:00 in the morning. PT is done O'dark thirty. For cadets that have to be there at 6, it means they leave at 5-5:15, and get up at 4:30 in the morning. NOT FUN!
Additionally host units traditionally have military fraternities and cadets are known to have social nights or hang in their lounges between classes. At DS's they have 3 military fraternities, they have weekly meetings from 6-9 at night once a week. These meetings do not occur on GMC night. That would mean if you want to be involved in the det., you now have 2 nights of traveling, plus ROTC days. It becomes difficult to juggle for 4 yrs, especially if you don't have a car for transportation you may not get that feel of camaraderie like cadets that at are at the host college.
OBTW a type 7 cannot work for high dollar IVY since they are capped at IS tuition rates, or something like 9K tuition, I am not sure on the actual dollar amount, but the fact is that is why Type 7 4 yr convert to Type 2 3 yr. Type 7 does not allow you to make up the tuition difference, Type 2 does allow it.