Holy straw man, batman! Let's take this one step at a time!

What will you do when companies begin the new wave of mechanization of the job field?

What "job field" are we talking about here? Fast Food workers? Because the fry machines at McDonald's have been automated for about 20 years. Most restaurant food, from "fast" clear to "formal", is essentially reheated leftovers created specifically for the service industry. And an ordering kiosk at the front of the line simply reflects that it's cheaper to have customers order their own food than pay someone $15 an hour to mash buttons. If you haven't been paying attention, grocery stores "automated" about half of their check-out counters over ten years ago so it's not like we're suddenly going to wake up tomorrow and the T-1000 will be wearing an apron.

Will you boycott Baskin Robins when their are no humans behind the counter?

People have been effectively boycotting Baskin Robbins since the advent of Starbuck's.

What should be done to ensure that people will be able to eat and sleep in homes and not on the street when this inevitably happens?

In examples of industrial displacement the usual response is extended unemployment, job retraining, and other work programs that may or (largely) may not assuage the issue. However, those are with skilled labor positions (generally they revolve around the collapse of regional heavy industry) and neither McDonald's nor Baskin Robbins employ skilled workers.

That's the crux: because they aren't "skilled" workers, the companies can pay them minimum wage. But since minimum wage hasn't been "living wage" for more than 40 years, those jobs externalize their social costs onto the surrounding community via food stamps, living assistance, subsidized healthcare, etc.

The drive for a livable minimum wage is about exactly this: companies should not be financially encouraged to provide positions that cost communities more than they bring in as revenue. The point of a $15 wage at McDonald's is that the human cost of a Big Mac is more than minimum wage. Once that gap is closed in the community's favor rather than the restaurant's favor, a bunch of shit shifts: prices go up, employment goes down, both sides piss all over each other in the newspaper, etc.

So whenever you see articles on Fox News about how something or other is "bad for the community" recognize that you're reading about something that is bad for a company's bottom line. Because here's the thing:

I'll bet there's research somewhere that says people aren't willing to pay as much for McDonald's food in a McDonald's without people in it. I'll bet McDonald's has research demonstrating exactly what their profit point is in an automated ecosystem. And I'll bet their robots are rolling out exactly when and where it makes financial sense for them to do so. And obviously they're not fans of the capital investment necessary to automate their service chain but in the end, they're a money-making entity and they will do what they need to do to make money.

Here's the actual debate: Do we want jobs that cost us more than they bring in in taxes? Because when you put it that way, the answer is an obvious "no." But when you put it that way, the guy who hires minimum-wage workers is going to change the subject 100% of the time.

Is it necessary for the good psychological wellbeing of members in a society to work for their necessities and luxuries?

Psychologically speaking, it's good for people to exercise skills and perform mastery in exchange for compensation they consider fair.

When "minimum wage" is a small fraction of "living wage" there isn't a single variable in the equation that even twitches the "wellbeing" needle.