τὸν μὲν ἄκουρον ἐόντα βάλ᾽ ἀργυρότοξος Ἀπόλλων -- You're right: when men suddenly drop dead (i.e., by a heart attack), they are said to be shot with an arrow by Apollo. (Apollo never misses when he shoots, by the way, just as Zeus always begets a child when he ravishes a woman, nymph or goddess.) Men are suddenly shot dead by Apollo; women, by Artemis. (Note that the English preterite/past participle of "strike" is "struck".)
τετίμηταί τε καὶ ἔστιν -- In the Oxford commentary, Hainsworth describes this as a "puzzling expression." Just as you thought, he suggests that the meaning should be supplied by τετίμηταί, and that τιμητή or τιμήεσσα should be understood. Garvie, in the Cambridge Green and Yellow series, rejects this interpretation, suggesting that ἔστιν is a textual corruption.
ἐκ -- Garvie cites a few other examples in the Homeric poems where ἐκ + genitive is used instead of ὑπό with the agent. LSJ ἐκ has a number of cites in various authors for this usage:
5. with the agent after Pass. Verbs, by, Poet. and early Prose, ἐφίληθεν ἐκ Διός they were beloved of (i.e.by) Zeus, Il.2.669 ; κήδε᾽ ἐφῆπται ἐκ Διός ib. 70; “προδεδόσθαι ἐκ Πρηξάσπεος” Hdt.3.62; “τὰ λεχθέντα ἐξ Ἀλεξάνδρου” Id.7.175, cf. S.El.124 (lyr.), Ant.93, Th.3.69, Pl.Ti.47b; “ἐξ ἁπάντων ἀμφισβητήσεται” Id.Tht.171b; “ὁμολογουμένους ἐκ πάντων” X.An.2.6.1 ; “τὰς ἐκ θεῶν τύχας δοθείσας” S.Ph.1316, cf. Pl.Ly.204c : with neut. Verbs, “ἐκ..πατρὸς κακὰ πείσομαι” Od.2.134, cf. A.Pr.759 ; “τλῆναί τι ἔκ τινος” Il.5.384 ; “θνήσκειν ἔκ τινος” S.El.579, OT854, etc.; “τὰ γενόμενα ἐξ ἀνθρώπων” Hdt.1.1
δειδέχαται μύθοισιν -- must mean something like "they welcome her with greetings". The odd form δειδέχαται is thought to be an athematic (μι-verb) present tense, not a perfect.