Because JEJ is genitive and dative while JĄ is accusative. Every verb or even context requires a specific grammatical case in Polish. For example the verb "dawać" (to give) can take both accusative (the object that is being given) and dative (the receiver). If you want to say "I give it to her" where "it" is a feminine noun, you'll say "Daję ją jej". Thanks to the cases we can get along without articles and with less prepositions.
It's the other way around. 'Ją' is used in affirmative sentences and 'Jej' is used in negative sentences and also to indicate possession ('Jej' = her, poss. pronoun). You have to be a bit careful though, because 'jej' (as I understand it) is only used in a negative sentence whose affirmative version uses 'ją' in the accusative case. For example: 'Kocham ją' (I love her, Accusative) -> 'Nie kocham jej' (I don't love her, Genitive). I hope this helps! Good luck!
Yes, but as I said, the genitive case applies only to negative sentences whose affirmative counterpart uses the accusative case. If for instance you had an affirmative sentence in the dative case, it would stay in the dative case in the negative sentence. You can check this page for examples: https://en.wikibooks.org/wiki/Polish/Noun_cases#Genitive
I hope you find this useful!
So if I understand well, ''ją'' is equivalent to the French ''la/l' '' you put before a verb and ''jej'' is like the French ''son/sa'' article?
''Mamy ją'' = ''On l'a / Nous l'avons'' ''Znam ją'' = ''Je la connais''
''Mam jej psa'' = ''J'ai son chien'' ''Jej wino jest dobre'' = ''Son vin est bon''
It's unfortunately not as straightforward but in most cases "ją" will indeed match the French "la/l'/le" for the feminine nouns, except for the negative sentences. "Jej" on the other hand always means "son/sa" but also "lui" (when it's in the COI function for the feminine nouns) and sometimes even "la/l'/le" if the verb doesn't take the Accusative case. Examples:
"Widzę JĄ tutaj." = "Je la vois ici."
"Nie widzę JEJ." = "Je ne la vois pas."
"Lubię JEJ psa." = "J'aime bien son chien."
"Daję JEJ prezent." = "Je lui donne un cadeau."
"Szukam JEJ wszędzie." = "Je la cherche partout."
I think that I understand that the pronoun ja in this sentence is the direct object and therefore in the accusative case. However, mamy, "we have" I assume is possessive. Therefore I thought that the pronoun following the possessive verb is suppose to change to the genitive case, in this instance jej. Where am I getting confused. Thanks!
When we think of 'possession means Genitive', that's about phrases like "Adam's watch", "my brother's girlfriend", "Anna's car" and so on - phrases which in English use Saxon Genitive. In those phrases ("zegarek Adama", "dziewczyna mojego brata", "samochód Anny" the 'owner' takes Genitive.
But it doesn't mean that everything that's connected to possession takes it. Here we just have the verb "to have", and it takes a direct object in Accusative. Moreover, if we are talking about "my car" or "your computer", that simply takes a possessive pronoun (mój samochód, twój komputer) and no Genitive is involved.