Interesting! I've never heard the male form used except specifically when talking about a male person. I'd guess it's a regional thing again (die/das Nutella anyone?).

But for the single mom/dad I've not heard that as a derogative in daily speech.

For me it makes sense to talk about a situation from the perspective of the people in the situation and not some circumstance.

“Single Mom” has become some kind of slur, understanding that correct?

Honestly it entirely depends on the context. Some see single parents as incredible superheros for how much they manage to balance everything and keep it all stable for their kids who are too young to be left alone. But also some use it as a put down, whether as slut-shaming, part of anti-poor rhetoric or there's the infamous "but where are the fathers?!" racial dogwhistle. Basically single parents are a convenient block of people to paint all sorts of different pictures of to push whatever narrative one might be trying to push