Oh, and the minimum wage is an entry level wage. You aren't supposed to be able to live on it because it's where you're supposed to start, not where you're supposed to finish. Minimum wage is for people with no experience and no developed good work habits. Once you get experience and good work habits, you will naturally get a higher wage. Unless you suck and are completely unemployable by anyone who values competence.
How could any nation possibly afford a "living minimum wage" when you are guaranteed to be able to eat and live indoors whether you are a McDonald's fry cook or a rocket scientist? No one would choose to be a rocket scientist if they could get their staples being a fry cook. People do not expend effort if you give them a meager existence guaranteed, especially if someone else is paying for it and they feel like they are entitled to it just by drawing breath and having a pulse.
I don't have much time right now, so I'll just tackle this bit for the moment.
You say it's fine that the minimum wage isn't enough to cover the bare necessities because it's an entry level wage and you'll supposedly move up out of that bracket quickly, but there are issues with that line of reasoning. Assume for the moment that whatever entity employs a given minimum wage worker consistently provides a 40-hour work week (which is in no way guaranteed) and that diligent work is to be recognized and rewarded in a somewhat timely manner (also by no means guaranteed). What is the worker to do in the intervening period between hiring and when their wage becomes livable? If the necessities aren't covered by the wages from one job, then said worker has a no-win choice. They can do without, which either has a direct negative impact on their health (if they can't afford rent and associated costs, have to eat a nutritionally deficient diet, or can't afford medical coverage) or an indirect health impact and a direct impact on their opportunity to improve their economic situation (if they can't afford a phone, this comes back to bite them pretty fast, and an inability to afford a car can be very problematic in some locales). The other choice is to take a second job, which covers the worker financially in the short term but brings up other problems (for example, sleep deprivation associated with getting more hours eaten up by labor has a detrimental impact on one's health and reduces the quality of one's work, which limits advancement and increases the risk of getting fired from one or both jobs). And this all assumes that the worker in question has no dependents and is not trying to pay for an education; either of those conditions makes it even more difficult to get by on minimum wage. There is a very real possibility - in fact, it's highly probable in a lot of cases - that one of these "entry level" workers will be stuck earning the minimum wage for an indefinite period. Unless and until they advance, the worker is stuck in an untenable economic position. How do you justify this, and if you do not, then how do you propose to fix the problem?
Quick correction regarding the rocket scientist/fry cook example: the assumption that no one will do anything more than they have to do is inherently flawed because it fails to take into account a number of other factors that push people to work at more intellectually demanding pursuits. A worker whose needs are adequately provided for has the opportunity for pursuit of the sciences, the arts, etc., and the chances are pretty damn good that something somewhere will capture the imagination and provide an incentive for study of that subject. (Peter Kropotkin explains this better than I can in The Conquest of Bread.) People are only lazy up to a point; stimulate their passions and their intellectual curiosity, and you'd be surprised what comes of it.