Can the mirena (levonorgestrel) IUD come out?

If the strings pulle. The Mirena (levonorgestrel) IUD is one of the BEST forms of birth control available, it lasts 5 years, is ~99.5% effective, and thins the uterine lining so that you get lighter periods. 20% of women will stop having periods after 1 year and that's perfectly healthy. Effects in the uterus and so it won't affect or be affected by other medicadtion; very safe method; biggest risk after insertion is expulsion (1-2%).
Yes. The expulsion rate is higher if it was recently put in. Check the string. If you or your partner cannot feel the string, see your doctor right away and use another type of birth control (e.g. Condoms) until then. You can also have your doctor take it out any time before the 5 years is up if you decide to try and get pregnant. Take care.