[1] The headword verb is common in epic: see Homer, Iliad 16.92; Odyssey 3.386, 8.4, 23.293, 17.372, al.; see LSJ s.v. at web address 1. For the headword itself cf. the Synagoge. For the gloss διοικῶ , cf. Etym. Genuinum (and ps-Zonaras 974). The gloss is ἀρχεσθαι in Hesychius, eta53 (Thucydides 3.61.2; see also eta91).
[2] No, imperfect (as translated here): imperfect indicative active, third person singular, with contraction (from ἡγεμόνεε ), of the verb ἡγεμονέω (see LSJ at web address 2). This is a less common variant of, but with the same meaning as, the headword, whose corresponding form of the imperfect would be ἡγεμόνευε . Though rarely, ἡγεμονέω is found in Plato: see Laws 631C, Timaeus 41Cc ἡγεμονοῦν , Timaeus 70c ἡγεμονεῖν .
For other misinterpretations of verbal forms see under alphaiota 323, delta 1250, epsilon 1849, epsilon 2503, iota 160.