неё is genitive (after У). What case is ней?

Дательный, творительный и предложный.
К кому? - К ней.
С кем? - С ней.
О ком? - О ней.
https://ru.wikipedia.org/wiki/Личные_местоимения

"У ней" is either archaic or colloquial form.

.שאלה יפה .לצערי, אני לא יודע התשובה

it seems, "ней" is genitive (after У) too, but colloquial.

תודה רבה על כל ההערות וההסברים.

Thanks. I had a feeling it serves two cases at the same time, but I wasn't sure which.
About more than ten years ago I could cite them quite quickly, but in the meantime I forgot, and it became passive knowledge ;-).

איגור, תודה רבה.
תיקון לשוני קטן: אם יש לך ה' - *ה*תשובה, אז צריך "את" לפני
אני לא יודע *את* התשובה.

@Eldad
If you are a fan of grammar, so:
У неё is genetive
К ней is dative
В неё is accusative
C ней is instrumental
О ней, в ней is prepositional.
As you can see, неё is genetive or accusative, and ней is dative, instrumental, or prepositional. Btw, most of Russian speakers don't even know such things, so I have no idea, if it's useful for learners or not...

"У ней" is colloquial form for "у неё". For me, "У ней много друзей" sounds natural, but it's not correct according to grammar rules, as I think.

תודה על ההסבר

as far as I know, "я зашёл к ней домой", "я пошёл с ней куда-то" is coreect.
"У ней есть много приятелей" is incorrect.

תודה על ההסבר.
המשפט השני למעלה פירושו:
הלכתי איתה לאנשהו - I went with her somewhere.
מה פירוש המשפט הראשון?
הלכתי אליה הביתה?

maybe better "נכנסתי".

נכנסתי אליה הביתה

תודה.
אעתיק את המשפט ברוסית, ואוסיף תרגומים בשפות שונות.

i think both correct, הלכתי and נכנסתי

Thanks, Selena.
Indeed, if you are a foreigner and wish to speak or write Russian, you have to know very well the падежи. Thanks for your comprehensive list!

You're welcome, Eldad.
Personally I don't pay much attention to grammar rules, but prefer learning "as is". But I'm glad, if the list is helpful for you.