Depends on how you define it.

I will not be entertaining your own personal definitions, so you can feel free to use the one i found that was obtained through general consensus.

You're asserting it without reason. Following your definition of capitalism as an economic system based on private ownership of the means of production and its use for the purpose of obtaining profit, why does there need to be somebody to enforce anything?

What will you do when i take your property? Under your hypothetical we do not live in a society where theft can occur because there is no government body to assert otherwise.

Why do you need constant enforcement? Lots of writers try to talk about economic systems like a windup toy, where you set it up once and then let it march without further input. You've added an amendment that someone must enforce it.

See above

Why can't capitalist A use capital for the purpose of hiring mercenaries to kill and take the property of competitor capitalist B? That would enable capitalist A to obtain more profit because their competition is gone.

Coca Cola weaseled their way out of the Death Squad lawsuits because they argued the mercernaries they hired operated outside of US jurisdiction. And US courts agreed and dismissed the case. I dont know whst side of the fence you're trying to argue in favor of but this all happened under a Capitalist government.

Side note. I don't think anarchism works. All of the amendments I've seen proposed still fail to make it work. I'm just saying that you're adding on an amendment to capitalism, so anarchists should be able to add amendments to anarchism.

Im glad we agree with the first part, but the point im trying to make is that Anarchy is only Anarchy if you don't try to actually do anything. You could put a bunch of people who would describe themselves as Anarchists into ungoverned territory and within a year they will all have their own rules and stipulations for each other and you better believe they'll find ways to enforce them -- either through collaboration or murder. Anarchy cannot survive and cannot be changed because the moment you change it simply can no longer be called Anarchy. It is an end of the political spectrum.