The problem with the US discourse on the subject is that it's a debate for/against higher minimum wages rather than a debate of "what regulations need to change so that the minimum wage without regulation is a livable wage".
Without EITC & food stamps and other assistance $2/hour wouldn't cover food & rent even working 2 jobs, so they'd be forced to turn those jobs and look elsewhere, most likely to crime.
EITC & food stamps to the employed are a subsidy for the employer and distort the true market price for labour. Perhaps less than a minimum wage does.
Unemployment does exist and it is not lethal.
I'm not sure what you're talking about. You are not supposed to receive state support while being employed.
From a political standpoint. It's also a lot easier for people to support. You have to work to receive it and it's been popular in both Republican and Democratic administrations. I can't speak for the current one. I don't think Trump has any core set of beliefs.
1. https://en.wikipedia.org/wiki/Price_controls