It's all relative. Someone making $250k with a family in the SF Bay Area could be basically living paycheck to paycheck if they just try to appear casually financially well-off. Nice house, nice car, electricity is 4x more than Idaho for example so add bills, eat out a few times, and send one child to a $4k a month 1st grade and you're living paycheck to paycheck.
No, that's just bad financial management. Spending $48000 to send your kid to a private school is a choice that parents can make when they're wealthy enough to do so.
"Living paycheck to paycheck" means that you just barely make enough to pay for food and rent, and don't have any spare money to cover unplanned costs like medical care. Spending a ton of money on vacation and private school is by definition not living paycheck to paycheck.
No it doesn't. Living paycheck to paycheck means you don't have any left over each paycheck, and the worse version of it is that you don't even have emergency savings left over in case unforseen costs come up.
This is absolutely batshit to someone living in the midwest. I could save enough to retire in 5-7 years if I were making that much.