it is very important to know that German language have 4 cases. The Possessive Pronouns are conjugated in accordance to these cases and genders. for instance conjugation of unser (our) for Masculine gender would be like this :
full chart is available at : https://deutsch.lingolia.com/en/grammar/pronouns/possessive-pronouns
which is derived originally from the main definite articles (der/das/die/dem.....) chart: https://upload.wikimedia.org/wikipedia/commons/thumb/5/5c/German_die_der_das_declensions.svg/775px-German_die_der_das_declensions.svg.png
i suggest to memorize the picture of the last chart. it will be useful.
What exactly are dative and genitive cases? I have researched them but don't understand them.
I am no native speaker, but here are my 2 cents:
die Nominativ Form: The nominative case is the "basic" form of nouns and articles. This is the form in which we usually see the subject of a sentence. He likes apples. Er mag Äpfel.
die Akkusativ Form: The accusative case is usually used to describe the object of a sentence, to which something is done etc. He likes him. Er mag ihn I think the majority of verbs in the German language require the subject to be in the accusative case.
die Dativ Form: The dative case is usually used to describe an object in a sentence to which something is given (some verbs also require this case, but they are fewer). He gives the apple to him. Er gibt ihm den Apfel.
Notice how you can see all three cases in the last example. 'Er' is in the "basic" case (Nom.), 'den Apfel' is in the accusative case (masculine nouns change their article, so instead of being der Apfel, it is now den Apfel) (Akk.) and 'ihm' is in the dative case (Dat.)
I am still in the middle of an A1 course here in Germany and we haven't learnt the genitive case so I couldn't tell you much about it.
I am very open to corrections, anyway, hope this helps!
Here's my two cents from studying Latin for a year. I think it should work similarly in German. Genitive case is used to show ownership. Example: The door of the house. "Of the house" would be replaced by the genitive case of Haus.