I moved provinces in 2018. I still have unused provincial tuition credits, but no Federal. Am I unable to use these provincial credits in my new province?

You can, but only up to the Federal amount. So when it asks you to enter “Unused provincial tuition and education amounts”, put the same as you have for the Federal amount. This amount can be found on your Notice of Assessment for 2017 from the CRA.

So I assume that if my Federal amount is 0, than I cannot enter anything for Provincial.

That's correct.