I'm in the process of kashring my kitchen. I almost only eat parve so it's pretty easy, and the kitchen is formally all milchik. However, I can't find any good instructions on how to handle a menstrual cup (neither here nor google). The problem here is that the cup needs to be sterilized now and then, to which one usually does with a saucepan on a stove. It's washed beforehand, but it's still an object that has had contact with blood. Would I need a separate saucepan and stove for this, or is there some other way to solve this?
The Shulchan Arukh YD 66:10 rules that consuming human blood is forbidden because of maris ayin, the prohibition of doing something that appears itself to be forbidden. The example he gives is that if you're eating a piece of bread and some blood comes out on the bread, you can't eat that blood. But if the blood remains in your mouth where nobody can see it, you may swallow it.
We see from this that the prohibition of eating human blood is not a kashrus issue per se. So sterilizing an item which has touched human blood and then already been cleaned should not be a problem at all.
There are plenty of reasons why this probably wouldn't be a problem even if we were dealing with animal blood, but I won't get into it since that's not the question.