“πότερον εκεινω παιδες ουκ ησαν διπλοι ους τησδε μαλλον εικος ην θνησκειν;”
1-What gender is πότερον here?
2-What is the meaning it imparts here?
3-Why is it in the accusative?
This is a question, look at punctuation at the end. The interrogative πότερον is neuter, used as an adverb. It is often used at the beginning of a sentence containing two alternative propositions. πότερον A ἤ B. Here the alternatives are not spelt out and is best translated as “Is it not the case that that man had two children…” or “Did that man not have..” The alternatives here are one of Menelaus’s two children or Clytemnestra’s child who was sacrificed by Agamemnon.
As MWH has recommended a good dictionary would be a great help to you. πότερον is quite a simple word and your uncertainty about it suggest to me that you are trying to read texts which are too difficult for current your level.
πότερον didn’t seem motivated in just this bit, so I looked it up to see context, and boy is there.
πότερον ἐκείνῳ παῖδες οὐκ ἦσαν διπλοῖ,
οὓς τῆσδε μᾶλλον εἰκὸς ἦν θνῄσκειν, πατρὸς
καὶ μητρὸς ὄντας, ἧς ὁ πλοῦς ὅδ᾽ ἦν χάριν;
ἢ τῶν ἐμῶν Ἅιδης τιν᾽ ἵμερον τέκνων
ἢ τῶν ἐκείνης ἔσχε δαίσασθαι πλέον;
ἢ τῷ πανώλει πατρὶ τῶν μὲν ἐξ ἐμοῦ
παίδων πόθος παρεῖτο, Μενέλεω δ᾽ ἐνῆν;
LSJ calls this four clauses, but maybe that’s based on a different text? I count three. The “ἢ τῶν ἐκείνης” is comparative, imo.
Two clauses is normal for πότερον, as it asks for one of two. So me that third option, ἢ τῷ πανώλει…, comes across as highlighted, really a new question that dismisses the previous two possibilities. This is the answer that she believes.