On this compound adjective and others from boh/, 'a cry (for help or for the start of battle)', and qe/w, 'I run, dart', see P. Chantraine, Dictionnaire étymologique 182-83, 433. These compounds are also used for remedies in medicine.
[1] This would be odd glossing for a headword transmitted as bohqo/on, i.e. an adjective in the accusative singular. Hesychius has it also, but with suitable glossing ("swift in the battle"), and Latte regards it as quoted from Homer, Iliad 17.481. As regards the Suda, though, Adler notes that boh/qoon was printed as boh/qeon in the editio princeps. Apparently the Suda compiler thought the headword was an unaugmented imperfect from a verb bohqo/w (or bohqe/w), to be distinguished from the verb bohqe/w that means "help."
[2] This is rather misleading: the dative with bohqe/w, 'I hasten to the battle cry for', refers to the person being aided while the dative with ma/xomai, 'I fight', refers to the person being fought against.
[3] Aristophanes, Lysistrata 353 (see web address 1 below for the text), with comment from the scholia there. Henderson in his edition ad loc. points out that there are two words e(smo/s, one apparently from e(/zomai and meaning any crowd that settles, such as a swarm of bees (apparently that intended here), the other from i(/hmi of streams of liquid such as milk and honey that are released. Is there by any chance a pun on women's milk that arrives at the cry of a baby, the only cry that (properly domesticated) women should run to?