The minimum wage question is interesting. Traditionally, we always assumed that higher wages meant fewer jobs. Seemed obvious. But then there are all sorts of harder to measure follow-on effects, like the fact that people have more money to spend and people at the low end of the wage scale tend to spend their money locally.
There have been some "natural experiments" where, say, a region raises the minimum wage and neighboring jurisdiction does not and generally the negative effects on employment are less than is usually projected ahead of time.
And then there's the question of whether or not jobs that don't pay a living wage in the first place should even get counted. In those cases, at the very least, we should roll in the government assistance (Medicaid, food stamps, etc) those people receive to calculate the true cost of that employee. My beef with this is that we effectively subsidize cheap labor for companies rather than making them pay the actual cost of those employees.
Then there is the problem that in SFO and NYC, $15 is in not even close to a living wage, while in some parts of the country, a full-time job at $12/hr might actually pay rent and food. I don't think there's anywhere where $7.25 is a living wage.
And finally... the hourly wage is just one small part of the puzzle. There's also the overtime threshold, schedule insecurity and all that that plagues low-wage workers.
Generally speaking, the US is not a good place to be low wage.