Careful when copying the text, JM: ἀσφακεία is almost a word! (-:
Your questions:
1. τινὰ τῶν τοῦ Ἀστυάγους and (τινὰ) τῶν ἐμῶν are parallel expressions: "one of Astyages' men" (and not) "one of my men" (needs to become his murderer).
2. μέντοι, "however," goes with the whole phrase, not just with δεῖ, which goes with γενέσθαι: "it is necessary for ... to become" (his murderer). Note that δεῖ is an impersonal verb, followed by an infinitive with its subject in the accusative case.
3. Not this time. Try again!