Is the US socialist because nVidia is a public company, therefore the shares are owned by the public? [...] The ownership of the company is shared, so it must be socialism, right? I’d say no, because it’s not shared evenly.

How did you mess up this badly? A "public company" [sic, the correct term is "publicly traded company"] is a regular private company where the owners are hundreds or even thousands of individuals. A publicly owned company is one where every single citizen owns the company simply by being alive or every single worker owns the company simply by working there.

What if a single individual owns a single “mean” of production, but everything else is owned by the state

I don't even understand what you mean by this...

Modern economies are mixes of socialism and capitalism. The people (through the government) own certain things, and individuals own other things.

No, they're not, and this shows a very serious hole in your knowledge of economic and social systems. While, informally, it's sometimes said to be the case, that's strictly an oversimplification to communicate a different idea. Countries like the US simply use a government-assisted capitalist model. Places like the Nordic countries have a more transitional system, but are ultimately still just capitalist.