They favored Alexander may be expressed as “Instead, they sided with King Alexander” (Contemporary English Version).

Because he had been the first to speak peaceable words to them is literally “because he had been to them prince/originator of peaceable words.” The obvious problem with the translation here in both Revised Standard Version and Good News Bible is that Demetrius, not Alexander, was the first to seek the favor of Jonathan (see verses 3-7). The following suggestions have been made for the phrase “prince/originator of peaceable words”:

1. “Prince of peaceable words” means that Alexander’s offer was better than Demetrius’; it was “first” in merit rather than in time (so Fairweather and Black, Dancy).
2. The original Hebrew text had a word meaning “gifts” (shillum) rather than the word for “peace” (shalom), so the phrase refers to Alexander as the Jews’ “leading benefactor” (Bartlett).
3. The original Hebrew text had a word meaning “inducement” (shillum) rather than the word for “peace” (shalom). New Jerusalem Bible follows this suggestion by rendering the whole clause as “since he seemed to offer the better inducements of the two” (similarly Abel)
4. The Greek word translated first can be rendered “originator.” Alexander can be called “the original cause of their opportunity for peaceful discussions” (Goldstein), since it was his invasion that set the whole process in motion.

Numbers 1, 2, and 3 all present the difficulty that the deal offered by Demetrius was quite a bit better than what Alexander had presented. The Jews simply didn’t believe him. Number 4 seems a little unlikely also, but of the options, we believe it is the most satisfying. So we suggest the following translation for the whole clause: “for they felt that only with him could they have any chance for peace.”

And they remained his allies all his days may be expressed as “and they remained his ally as long as he lived.”

Quoted with permission from Bullard, Roger A. and Hatton, Howard A. A Handbook on 1-2 Maccabees. (UBS Helps for Translators). New York: UBS, 2011. For this and other handbooks for translators see here.