A trans parent would likely still want to be called “Mom” or “Dad”, I assume. At least that’s the case with the few trans parents I know.
Parents don’t usually use “daughter” or “son” as pronouns, so I don’t think it would come up with non-binary children.
Do children of non-binary parents call their parents by their first name? It seems unlikely that they say “Parent, may I please have more screen time?”.
No you have it backwards, it’s DOM. As in, “I was bad so my dom had to punish me.”
No clearly it’s MOD. “I was bad to my mod timed me out”
Well that can’t be because I call my nonbinary wife Daddy!