In the U.S., the federal minimum wage is established by the Fair Labor Standards Act (FLSA), as amended.
You don’t have to cross state lines to be engaged in interstate commerce. Since the New Deal interstate commerce is understood to be affected by commercial transactions that occur within a single state’s borders, and the argument that your commerce is wholly intrastate is almost always a loser. The federal minimum wage applies to almost every private company in the U.S. that has employees.
The whole point of the minimum wage is that employers and employees cannot agree to undercut it. As a society we’ve decided that’s exploitative of workers, and so we’ve circumscribed the types of bargains labor can strike with their employers. If a company could avoid the minimum wage by simply finding employees who agreed to take less, then there wouldn’t actually be a minimum wage.
But this doesn’t mean that every worker has to be paid $7.25 an hour. As noted above certain occupations can count as tipped, which has a lower wage paid from employer to employee so long as tips make up the difference. Some jobs are exempt from the FLSA, so you don’t have to worry about minimums or overtime at all. But these are typically professional or managerial services, and you can get in big trouble by nominally classifying a labor job as managerial just to avoid the FLSA. (It’s exceedingly rare for an exempt job to pay less than the minimum on an hourly basis – maybe it doesn’t legally exist at all. Overtime is typically at issue in the exempt/non-exempt distinction.) And independent contractors aren’t covered by the FLSA – although again, just calling someone who is really an employee an IK for purposes of avoiding the Act can get you in big trouble.
The other important issue is, as mentioned, state law. States may have higher minimum wages, or they may have a minimum that covers more employees than the FLSA. States may also have a lower minimum, in which case the FLSA governs in most cases. Occasionally state government employees might not be covered by the FLSA (not sure of the contours of this), so they’d be under the state minimum, even if it’s lower than $7.25.
As to the particular questions in the OP: I don’t know about the first one. I think that the FLSA allows some in-kind compensation, but I don’t know the precise limits; I’m sure there are some. Note also that even if the FLSA allows it, state law might have a sifferent rule. But even if compensation in kind is included, it would still have to come up to the value of the minimum wage.
As for the second, hell no. Benefits aren’t wages. There’s no general rule requiring employers to provide benefits (although in the future there will be penalties for certain employers who don’t provide health insurance). Benefits are provided b/c employers think they’re a cheaper way to compensate employees than cash (which, given the advantaged tax treatment for employer-sponsored health care, they are). But any benefits the employer chooses to give are on top of the minimum required cash money they have to pay you under the FLSA.