What does "τοὺς τροπους" mean here?
Plural, accusative of respect. "With respect to his ways (i.e. his character)." Looks like you looked up τόπος instead of τρόπος.
μηχανᾶται is not a participle. It is a third person singular, present middle indicative verb.
τῶν ἐταίρων is
plural. Again, JM, review your second declension.
λύσᾱς is an aorist active participle, masculine singular nominative: "having dissolved," "after dissolving."
πᾶσα πόλις = every city
πᾶσα ἡ πόλις = the whole city
P.S I like the way you translated που here.