"These are my son and daughter" as suggested by Flanders1.
"In regards to the conjunction "and," whether or not the two objects are singular or plural doesn't matter: the verb should automatically be plural because the word "and" denotes that there are two things". ~ quote from https://painintheenglish.com/case/52
I would say "These are my child and nephew" is correct.
"A compound subject whose parts are joined by and usually takes a plural verb regardless of whether those parts are plural or singular." ~ quote from http://www.learnersdictionary.com/qa/compound-subjects-and-verb-number
If you want it to be in singular mode then maybe you can say it this way "This is my child and this is my nephew".
Unless you've got a weird family tree and the child/nephew are the same person...
Yes. "These are my child and nephew" Is correct.
However it's more natural to say either "this is my child and this is my nephew" or "these are my child and my nephew" while pointing out each individual.
Haha it depends on how deep you want to go!
In this example? My English instinct is to say "these are my kids", but since we're going for a more word-for-word translation, I would say "these are my son and daughter", I would NEVER say "this is my son and daughter".
If you wanted me to explain what makes something correct, that's way harder to say. With language, I generally go with: what would you commonly hear from a native speaker. Of course, romance languages like French, Italian, Spanish came from "improperly" spoken, regionalized versions of Latin. Every language is on its way to becoming a new one, what's wrong by the old rules may become a rule in the new language.