meaning of "leave me alone"

I understand this to mean to stop bothering me or interfering with me, however, does it also mean to ignore me and pay no attention to me ever again?

For example, I said to my brother, who kept interrupting me and trying to distract me while I was playing the piano, "leave me alone." Is it correct for him to tell me 1 hour later that he will not listen to me when I ask him to walk the dog because he is following my command to "leave me (him) alone"?

I thought leave me alone means stop talking to me or bothering me, but not to ignore me? IF I say "leave me alone" does this mean to ignore me should I seek your presence or help in the future?

"Leave me alone" has a pretty literal meaning: it is a command to leave (go away) so that you're alone (with the implication that the person should also not bother you). It doesn't have anything to do with whether you pay attention to a person.

Your brother's interpretation is, therefore, objectively wrong: he is not merely leaving you alone (by not bothering you), he is also ignoring you, which you did not ask him to do.