In economics, a free market is an economic system in which the prices of goods and services are determined by supply and demand expressed by sellers and buyers. Such markets, as modeled, operate without the intervention of government or any other external authority. Proponents of the free market as a normative ideal contrast it with a regulated market, in which a government intervenes in supply and demand by means of various methods such as taxes or regulations. In an idealized free market economy, prices for goods and services are set solely by the bids and offers of the participants.
It’s not equal to lawlessness, but it is lawless within market. These two are not equivalent. Still, that is not to say it is without order. Free market is entirely an economic system and not a social system nor any other plethora of systems in a country. So the topic of those other systems are simply out of the scope. Therefore, laws can exist in the society.
Robbery is part of the free market. Along with whatever happens like tornadoes, fire, murder, etc. Including the cost to hire your own security if necessary. Police is against free market because it is an intervention by the government. There does exist a grey area like if a robber becomes a gang and becomes a businesses’ external authority. Then they are impeding on the free market.
This is how free market is defined. So, to reiterate, if there exists any body that is redistributing your profit, it is against free market.
Communism is not a share of labour profits. Communism is more than just an economic system. It’s also a social and philosophical one. But assuming we’re only talking about the economic parts, it still doesn’t mean to share labour profits. Quoting wikipedia once again:
Communism is […] a socioeconomic order centered around common ownership of the means of production, distribution, and exchange that allocates products to everyone in the society based on need.
The keyword here is common ownership. Everyone owns the entire chain of production together. Your view on the concept of profit even existing is out of line with communism. From wikipedia:
Monetary relations in the form of exchange-value, profit, interest, and wage labor would not operate and apply to Marxist socialism.
If we go with Marxist version, you already own everything together and nothing has monetary value. You can’t have profit because there is no such thing as selling, and there is no money, so you can’t profit on anything. The concept of the profit sharing would be anti-communism.
If we go with Lenin’s view on state capitalism (which he said is not communism, but may be a necessary transition state to communism) where we accept that things have value but that only the state engages in capitalism, people still wouldn’t get profit. Because people still wouldn’t have money. You would simply have better status in livelihood in hopes that the state has used that money well for the benefit of the people.
Communism is not profit sharing, its very core purpose is to remove the concept of profit.
Sharing of labour profits at a nation level is called “labour share”. And at a company level, it is called “co-operative business”.