BUT if they are considered employees, don't they have to be paid at least minimum wage? Since they don't work for tips, it's not like they could be paid less and make it up with tips unless boosters get involved-- "hey Braxton, that was a darn good game there, lemme tip you $1000 here. Beat That Team Up North and it will be $10,000." Anyways, paying all of the varsity athletes would still impact the budget.
I doubt minimum wage would become an issue. For example, say these football players are working 50hrs a week for 50wks a year (which is probably more hours than they're actually working on strictly football stuff) and their scholarships amount to $35K a year (once against, a guesstimate, but 20K a year for out-of-state tuition plus 15K for room and board is pretty reasonable). With these numbers, the players are making $14/hour, which is almost double the federal minimum wage and still well above the highest local/state ones.
As for the other two items, the details are definitely tricky, but that doesn't mean they can't figure that out and find a solution that works better for the athletes and still protects the interests of the universities to an extent.