Correct. And we would still get plenty of "legal" immigrants...

Some people do not want to change their preconceived thoughts no matter how many people show them they are wrong

The higher cost of borrowing filters into prices too

Cheap money encourages spending = + inflation, expensive $ discourages spending reduces demand less inflationary pressure

That is only f you are spending your own money. "People" that spend other's money don't care.

It affects prices, but not inflation. If you pay cash for a house or car, the prevailing interest rates are irrelevant.

Again: Inflation is literally a relative increase in the money supply, AKA federal money printing.

Investopedia

If a companies borrowing costs go up they will do their best to increase prices for their product. That is inflation

The effect is the same in any event " One's demeanor at the feast depends on who's ox was gored to produce said feast"

Low interest rates stimulate spending, economic activity, higher rates cool down the economy , that why the fed adjusts the interest rate, if any cost go up it will of course put pressure to raise the prices of goods and services business , taking out a loan for day to day expenses doesn't sound like a winning business plan, taking out a loan or floating a bond issue to expand a business, different, high rates discourage that depressing economic activity

No, it isn't. Did you read the linked article?