I have in the past lived for years off of far less than the Federal minimum wage. It helped that I was healthy and didn't have any medical expenses- but the ridiculous cost of health care is a different debate...

Are any of housing, hygeine products, food, clothing , transportation or internet expensive, or is it just healthcare costs that are out of control?

Food in the US is incredibly cheap. Not high quality at the cheap end, but incredibly cheap. Same with clothing.

Last i checked they had increased the minimum wage beyond what trained heavy equipment operators were making. That is absurd, no matter how you slice it.

No, it's not. For one, other people having things worse off does not mean that certain people should not be trying to better themselves. For two, if that were true, then the heavy equipment operators should be asking for raises, as they now have the leverage to go to a less demanding job for more pay.

How can someone earn less than the minimum while in work? Is the minimum not required to be paid? If that is the case, what is the minimum for?

Do you mean absurd that trained heavy equipment operators are making so little?