shuvavim

Question

1)my brother-in-law has taken on the custom of fasting during this period of time. Can you kindly tell me the origin of shuvavim fasting? Is there merit for regular people like me in doing this fast? 2)my wife would like to know if it is permissible for her to take a co-ed yoga class. She is always modestly dressed. If the teacher, a man, touches her to adjust her position, is that a problem? thank you so much for your time.