"You are not the father."
Translation:Tu non es pater.
Est is 3rd person singular. It means is. You use it with he, she, it, and singular nouns. Es is second person singular. It means you are. You use it when you are speaking to one person about himself, for example: you are talking too fast, you are my friend, etc.
Hope this helps.
Non es pater, Pater non es, which one is more like "you are not (a) father", and which one "you are not the father" (the father of this child, implied), yes, I know, it's about context, but there's certainly an emphasis difference.
Would other word order possible (I read it was possible, but it gives a myriad of possibilities): Non tu es pater, Non es tu pater, Non es pater tu, etc...
Which ones are weird? Apparently, it's not wrong to unlink "non" and "es": Non es pater, Non pater es.
Does someone could explain me the difference in emphasis in those cases?
"Es" is the 2nd person singular present active indicative conjugation of "esse". There is a subtle but important distinction between "it means 'you are'" and "it means 'are' but it only goes with 'tu'".
Yes, the subject pronoun was omitted more often than not because the verb conjugation implies the subject pronoun. Inclusion was generally reserved for emphasis.
Redundancy is not inherently a bad thing. I'm not saying "always be redundant", I'm just saying there's no need to treat it as though it were grammatically incorrect.