Yes. And yes.

There's some Mammillaria in flower every month of the year, and M. plumosa flowers typically heading into winter.

Almost all Lithops, and a good chunk of the other mesembs, flower in autumn.

In Calif. a lot in November. I guess that would correspond to the time that they flower in Africa's Spring and Early summer. DNA at work here.I got there on Sept.9 and none were in flower yet, wasn't hot enough. Norma

November is Autumn in California. This corresponds to Autumn in the southern hemisphere. Plants don't know what month it is, just what season it is.

I have a mammilaria rhodantha that is two inches wide and four inches tall. sadly, it appears to have base rot and I fear that my only options are to either cut it in half and try to root it or just throw it away. Can it survive this kind of surgery???

you should be able to re-root that mamm. I have one that I've had to root twice now. Good luck!