How does a woman atone for an oath she swore to her husband? Is it considered a false oath (yamin ghamus)? How does she atone for many previous oaths that she did not fulfill and whose number she does not know? Is it permissible for her to give charity instead of expiation?

You erred by informing your husband about what occurred with that woman, and your husband erred by asking about it. You should have advised her and concealed her secret, because prying into the private affairs of Muslims is prohibited. You should have used dissimulation (Tawriya) instead of outright lying. The oath you took is considered a Yamin Ghamus (a false oath taken knowingly), but if it was to ward off harm from a Muslim woman, then many scholars hold that there is no sin in it. There is no expiation for Yamin Ghamus according to the majority of scholars, but Al-Shafi'i and Ahmad consider it obligatory, and that is more cautious. As for the previous oaths that you broke and for which you did not offer expiation, you must offer expiations for them according to what you most likely estimate their number to be. You must also repent to Allah and avoid frequent swearing.