Is it possible to get pregnant with a mirena (levonorgestrel) coil? Having quite a few symptoms and period is late. Posted a question yesterday but wasn't much help.

Very rare. Mirena (levonorgestrel) iuds are very effective with very low failure rates. You could simply take a home pregnancy test and in minutes you will have your answer. This is what your doctor would do. If positive it's important to be seen immediately due to the risk of tubal pregnancy.
Yes. No birth control method short of abstinence is 100% foolproof. However, Mirena (levonorgestrel) is highly effective and pregnancies are rare. Get a pregnancy test if in doubt.