true or false, first amendment rules don't apply to private companies.

The first amendment prohibits congress from making any law to prohibit free speech, so that means the federal government isn't allowed to restrict speech. However, there are exceptions such as speech to cause a riot, insurrection, obscenities on public airwaves, etc. all of which are not allowed.

In contrast, a private company like Twitter has the choice whether or not to allow or ban a certain post. The first amendment of the constitution does not apply to companies such as this one. On one hand, you could argue that such restriction is a bad thing because it limits speech; but you could also argue that if the government forced companies like Twitter to do a certain action, then it restricts their freedom.

For privately owned social media companies, their platform is something they solely own 100%, meaning that the government does not own or control what goes on that platform. So this is another viewpoint as to why the first amendment doesn't apply to these companies.

In a slight bit of confusing terminology, a private company can be publicly owned. This means that the government doesn't control the company, but rather it's traded on the stock market. Those who own stock in the company are part owners of it. You would have to use the phrasing "government owned and government run" to indicate that the government has full control of such a platform.