A literal free market is one without regulation. If you want a regulated market, don't call it a free market.

No, that's anarchy. A free market is one where market forces are allowed to work. A market captured by monopolists and anti-competitive agreements is not free at all.

Take a small market store selling product A and product B. Whichever sells more at a given price wins more profit, great. Free market forces are at work. But then (anything goes, after all) the manufacture for A comes in and says to the store owner: if you sell product B we'll firebomb your market and kill your dog. So then the small market stops selling product B. Now, the small market only sells product A and at a huge markup.

Is product A actually better? Does the consumer win?

Regulations are necessary so the manufacture of A can't do that and make sure that the market is actually free.

That's a well-regulated market not a free market. I completely agree that regulation is needed, and better by the people than by the biggest bully in the market.