Mamzerus is only created by Biyas Issur.
That’s correct. IIRC, R. Moshe paskened that artificial insemination from someone other than the husband does not create a mamzer because there was no Biyas Issur (although he says that, if at all possible, the husband’s sperm should be used).
If a woman has two husbands B’heter, then a Mamzer can not be created.
Ah, but that’s the magic question… if there can be said to be a cardinal rule of Jewish marriage law, it’s that a woman cannot be married to two men at the same time. Saying that she can have two husbands at the same time is such a major chiddush (and that’s a huge understatement) that you need to have *really* good sources to allow it.
The Wolf