Not quite. It would be a free market if people could freely move across borders. The overall arrangement that we have - where goods and services flow almost freely, but the movement of consumers and labor is restricted - is inherently abusive.
Kinda, but this is also how the free market dies—happens little by little. A change here, a law there that helps the people, oops, now the law makes it harder for competition to get in, and so on and so forth.
The business models this regulation harms are the business models that aren't desired to begin with. As such, a competitor is encouraged by regulation to find another, compliant angle to deal with monetization.
And competitors that already do that get an uplift (over time, but still).
Btu a free market (which is devoid of anti-competition regulation) also makes it harder for competition to get-in. Not to mention the problems of regulatory-capture (see: Boeing and the FAA).
It's almost as if the best (or rather: least-worst) option we have lies somewhere in-between laissez faire capitalism and mandatory state-ownership of all industry...
I don't think even the most well-intentioned state have the incentives to properly allocate resources in the market. Usually, when state-owned industries fail, the taxpayer suffers, so the administration has little to no incentive to actually do good in the long run.
It's not a 1D spectrum. You can have laissez-faire arrangements that still preclude massive concentration of capital (and thus effectively gut capitalism) without going all in on public ownership of everything. The key thing to remember is that private property rights themselves require some kind of government to maintain by using force when necessary - i.e. the existence of private property is inherently a step away from true "laissez-faire". Thus the government doesn't need to aggressively collectivize anything to avoid concentration of capital; it just needs to refuse to protect such concentrated capital.
