I love spinning, but I can see where daily spinning would get monotonous. I most like the social atmosphere of my class and gain a lot from it. One problem with spinning is that there really are no goals to set, and I find setting and reaching goals very motivational. Try cycling outdoors or running. With these you can set milage and/or speed goals that may motivate you.
Exercising during TOM? I don't know, I've never had a problem.

If cramps are a problem I've always found that the extra intake of oxygen actually helps.