Questions & Answers about В гараже стоит машина моего брата.
Why is it в гараже and not в гараж?
Because it describes location (where), not motion (to where). In Russian, в + Prepositional answers где? (where): в гараже. If you mean movement into the garage, you use в + Accusative answering куда? (to where): в гараж.
What does стоит mean here? Why not just “is”?
Стоит is the 3rd person singular of стоять “to stand.” Russian often specifies an object’s position: cars and other upright objects typically стоят (stand), books on a shelf often лежат (lie), pictures висят (hang). Here стоит means “is (standing/parked).” You could also say находится (“is located,” more neutral/formal) or припаркована (“is parked,” participle).
Why is it моего брата? What case is that?
It’s the Genitive case to show possession: машина моего брата = “the car of my brother.” Both words are in the Genitive: моего (Genitive masculine/neuter of мой) + брата (Genitive singular of брат).
Why not моей брата?