No, it's perfectly fine. In fact, it helps with cramps. Just lay down a towel and have at it. Be sure to still use protection.
Nothing wrong or unhealthy with having sex whilst on a menstrual cycle.
Just very messy. And it depends on you and your partner if you want to do it whilst on your period. Do it at the start of the period when it is fairly light or starting to trail off, otherwise put a towel down so as not to mess up your bed (or whatever).
Sexual intercourse is not dangerous at all during your period. Some couples actually prefer it. It can ease the pain of menstrual cramps as well. Just keep the condoms handy, and the shower ready. :-) Blessings - Blu