Karen
Women who are menstruating are considered ritually unclean in many cultures, including most of the Middle East, where Judaism has its roots. No one knew what was occurring at that time; all they knew was that, for some inexplicable reason, women would bleed, and there would not be a visible wound. After the menstrual cycle is completed, women visit the mikvah, or ritual bath, to cleanse themselves. Until that happens, anyone they touch – specifically, adult males – also become ritually unclean and must also visit the mikvah.
Wearing a wig is a sign of modesty – only a woman’s immediate family is supposed to see her bare head. This is more of an Hasidic custom than pure Orthodox Judaism. The Hasidim are a sect of Judaism that came from central Europe, and habitually the men wear dark suits with white shirts and no ties, and the women wear dresses below their elbows and knees. Both genders keep their heads covered to respect G-d.
Your last question involves kashrut, the kosher laws. If your friend’s parents do not keep a kosher home, then none of the food or utensils there are kosher, either. This affects mainly meat and dairy products; fresh fruit and vegetables that have not touched any utensils in the home are still kosher, as are any packaged goods with the appropriate markings (K, P and U are the most common). She can eat in their home, but only if the food is kosher, and only touched by disposable utensils that have not been used for any other purpose. This includes all forms of cookware.