Whiston is basically O.K., though free and somewhat over-extended. Let's look first at his translation:
and suggested to them, that they should direct their strokes against his head, that being the place wherein lay his mischievous designs towards men, and it being easiest to take vengeance on him, that way. Now here's a more literal rendering:
... and having instructed them to bring their blows against the head, seeing that the harm to humans lies in that (head), and seeing that its death will be easiest in that (head) for those who are defending themselves (against the serpent).Now for your questions:
φέρειν - gender singular/plural of who is acting
φέρειν, "to bring," is an infinitive dependent on ὑποθέμενος, "having instructed." Infinitives are verbal in character, Josephus, and have no gender, number, or case, though they're sometimes (not here) treated as neuter singular nouns. The actor in φέρειν is the same as the actor in the participle it complements, ὑποθέμενος.
ἐσομένης - ditto
This word is a future middle participle of the verb εἰμί, "be." It's genitive singular feminine because it modifies the genitive singular feminine noun τελευτῆς, "death."
Why genitive? Both τοῦ κακοῦ κειμένου and τῆς τελευτῆς ἐσομένης are a construction known as the
genitive absolute. This construction is absolutely independent, grammatically, of the rest of the sentence, and ordinarily consists (as here) of a noun plus a participle. Very literal translations of both would be something like "the evil lying" and "the death about to be being," but of course your English translation will employ various ways of expressing it: "since the evil lies," "because the death will be," etc. If your teacher has not yet told you about the genitive absolute, and is already having you read Josephus, you should fire him/her. Alternatively, look it up in whatever Greek grammar you're using.
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