Can the mirena (levonorgestrel) be moved during sex?

No: Sex can not dislodge a correctly placed iud. The iud is firmly implanted inside the cavity of the uterus. The uterus can expel an iud but this only occurs at a rate of around 1/1500.

No: 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%).