"Mom has a brother."
Translation:У мамы есть брат.
and checkout "Морфологические и синтаксические свойства", you'll have all of the gramar cases listed for a certain word.
Now, if you don't know when or in which situation is some particular grammar case used, you would need to read about them a bit :-)
Here's the good link for start:
Generally, I would suggest you not to remember those rules that much, but rather to try to remember phrases, and after you've repeated 1000000 phrases too many times you will learn to use the proper case when needed.
Also, bear in mind that's one of the things even many native speakers tend to miss the proper case from time to time (ok, usually the ones bit less literate ;-) ), so it's not a really big deal if you don't learn them perfectly, and most of the foreigners never do :-) (Source: I am one of those foreigners living in Moscow haha)
I also like the trick memorizing cases from this guy ;-)
Also I tend to listen to this girl every day a bit (I just minimize the window, she just has a weird look, which creeps me out :) :
She sounds repetative (on purpose), but it helps stucking those words and phrases in your brain
In previous genitive sentences like "У меня есть яблоко" the site also accepted as an alternate answer "У меня яблоко".
Is it also acceptable to remove "есть" in this setting and disambiguate the object from the possessor by case? Or is it only OK to remove the "есть" in the specific case of a genitive pronoun and not a genitive noun?
I can also tell you that Ruskies tend to drop "У тебя" part far more often than "есть" , especially when they're lazy and/or try to remove personal pronoun (Tebya/Vas) from things.
So for example if you're in the supermarket, because the cashier asks that question 1000 times per day, he/she will ask always you "Карта магазина есть?" (Do you have the store discount card) , rather than asking "У вас есть карта магазина? ", making things impersonal, like not having to address you with "Ты" or "Вы".
I wouldn't say "У меня яблоко". It might be grammatically correct, but people just don't say it like that. To me, it sounds like "У меня водка в холодильнике", a bit rude. It's possible to omit "есть" when the speaker is focused on the place where he keeps the object. It can be used between children, imagine a game: - I have an orange. // - Me - an apple.
I was taught that the есть was necessary when the existence of the thing was in question. So if you want to know who has the ball that you are tossing around with friends, you would leave out the есть. In my mind it corresponds to direct and indirect article usage. You would say "Who has the ball?" when the ball was already known. But you would not say "Does mom have the brother?" to ask if she has a brother. However, if you have a brother and you want to know if he is with Mom... can you say "У мамы брат?" I think so, but I hope someone will tell me.