question

Emlékszem, amikor
I remember when

Emlékszen ött ---?
I remember him - Emlékszem rá

This is my main question, how do you say:
I remember her - Emlékszem rá
I remember him - Emlékszem rá

The Hungarian language doesn't have separate masculine (he) or feminine (she) forms for the third-person singular pronoun (nor does it have any other kind of grammatical genders). The English phrase "I remember him/her" takes an object, which would be literally translated as "Emlékszem őt", as you originally wanted to write. But in Hungarian, the usage is different. "Emlékszem rá" would be literally "I remember on(to) him/her".