Capitalism relies on the state to enforce private property rights. The free market then naturally influences your government, which in turn naturally influences how people organize their lives. So yes, capitalism influences how people and communities organize themselves.

Also, capitalism itself needs to be guided, or it will escape and ruin the rules until it's no longer capitalism, except in name only.

Wouldn't guiding a free market be opposed to the concept of a free market?

Anti-trust laws, for example. Safety and environmental regulations.

Yes. In some sort of ideal world, where corporations would never dream of regulatory capture, abusing a monopoly position, finding ways to keep upstarts out of the way.

In the real world, capitalism is an unstable system. The "winner" gets too close to the state and then tries to shape the rules so they fit the incumbent and discourages everyone else. Boeing and the FAA is a recent high profile example.