Could someone explain the "male" and "female" versions of my in this sentence, particularly what it is referring to? (i.e. मेरा, मेरी, रहा)
Hindi possessive adjectives (मेरा, किसके, सबकी, etc.) change forms depending on the gender of the possessed entity, not the possessor.
For example, in the sentence ये मेरी किताब है, the feminine possessive adjective मेरी is used not because of the gender of the speaker (which, by the way, cannot be inferred from the sentence) but because किताब, the possessed entity, is feminine.
So, the possessive adjective and the verb in the sentence मेरा भाई मेरी बात सुन रहा है are in their masculine form only because of the masculine gender of भाई. The sentence will remain the same whether it's spoken by a man or a woman. Replacing भाई with a feminine noun, however, requires changing the adjective and verb forms: मेरी बहन मेरी बात सुन रही है.