Would I still have to pay tax in the US if I don't live in the US and was only there for a couple of months to play a character in a film.?

You'd only have to pay US taxes on the $ you earned in the US. But if a US studio cast you in a US funded film the likelihood is that it wouldn't even shoot here. This is why working actors have business managers and accountants who handle their finances. A typical actor might work in Canada, New Zealand and Romania all in the same year so there are experts in this type of tax preparation. 

Only on the earnings from a US source.

You would pay US taxes on your US earnings while 'living' in the US once the company booking you got a visa for you to allow you to live/work in the US while filming

Yes you will I think

The general rule, everywhere in the world, is that you pay tax on income where it arises and also where you are ordinarily resident.  So if you are British and normally live in the UK but spent 3 months in the US making a film, you will pay tax on that film income in the US.  You may also owe tax on that money in the UK but will be able to offset any tax you already paid.  For that specific year you will need to file both a US and a UK tax return.

No; only if you're resident there, or a citizen living anywhere

If you earn money in the United States, you will be taxed on this. Paying taxes has nothing to do with being a US citizen; it doesn't even have anything to do with working legally.

But for a production company to hire an actor from another country to play a role and jump through all the hoops to get you a work visa, you'd have to be a movie star in your own country first. Otherwise such role would go to somebody who is living in the United States already.

Because you were employed in the US.