Are gargling and sniffing obligatory when purifying oneself from menstruation, and is it necessary to re-perform the prayers missed due to ignorance of their obligation?

Your previous ritual bath (ghusl (definition)) is valid, and you are not required to repeat the prayers. The preponderant opinion is that rinsing the mouth (madmadah) and nose (istinshaq) are not obligatory in ablution (wudu) and ritual bath (ghusl), based on the Prophet's (peace be upon him) saying to Umm Salamah: "It is sufficient for you to pour three handfuls of water over your head, then pour water over the rest of your body, and you will be purified." The inside of the mouth and nose are not considered part of the outer body. Those who deem them obligatory have cited the hadith (definition): "Under every hair there is Janabah (definition) (major ritual impurity), so wash the hair and cleanse the skin," and Ali's hadith: "Whoever leaves a spot of hair from Janabah without washing it, will be dealt with such and such in the Fire." However, the majority refutes this with the verses: "wash your faces" and "if you are in a state of Janabah, then purify yourselves," and with Abu Dharr's hadith: "And when water is found, let it touch his skin," and "skin" refers to the outer layer of the body.