If you have a "This is X" sentence, it starts with "To" (regardless of the grammatical gender and number), follows with "jest" (singular) or "są" (plural) and then the noun case is in Nominative.

https://www.duolingo.com/comment/13539270

I don't understand your question. There is no word "moj" or "muj", "mój" is always with "ó".

mój is singular masculine nominative, and vocative. For masculine nouns that have singular accusative=nominative (masculine not animated nouns), it is also accusative.