I think they're flowering because their natural habit is SOUTH of the equator and right now it would be spring there, plants sometimes do that.

Try cutting the plant where it's not "dead" and re-rooting that part by waiting a few days for it to callus and putting it in soil.

Hello! I started growing cactus about an year ago. I am 13 years old right now. I like to collect rocks and minerals and going to mines......and I like cacti! (Ariocarpi especially). I joined when I saw that this is a good area to learn new things about cacti. So HI! see you in the fourms!