Questions & Answers about Мама не даёт мне гулять вечером.
Because мне is the dative case of я.
In this sentence, давать is used in the pattern:
кто-то даёт + кому + infinitive
So literally it is something like:
Mom does not give to me to walk/go out in the evening
That sounds odd in English, but in Russian this structure means to let / allow someone to do something.
So:
- мама = the person doing the allowing
- мне = the person being allowed or not allowed
- гулять = the action
That is why мне is correct here.
Yes, давать basically means to give, but in Russian it can also be used in the sense of to allow in constructions like this:
давать кому-то что-то делать
So:
- Мама даёт мне гулять = Mom lets me go out
- Мама не даёт мне гулять = Mom does not let me go out
This is a very natural Russian pattern.
A closely related verb is позволять = to allow / permit, which is a bit more formal:
- Мама не позволяет мне гулять вечером
That means nearly the same thing.