In my imagining of the universe Hector's surname is Ruiz. Partly because he like Mexican food, so it makes sense to see him as of Mexican (and more remotely Spanish) descent; and partly as a reference to Carlos Ruiz Zafon, whose 'Cemetery of Forgotten books' recalls Hector's preserving the books banned form the library.
To the second, that being easier: no, I don't think he was lying. It seems likely there was an old connection between VFDepartment and VFDevotees, and he was recruited from there.
To the first: this is a big mystery which we have had to ponder since WCTBATH came out. There does seem to be a tendency in VFD by the time of ASOUE to avoid action whenever possible; and he may not have trusted the Baudelaires because they had lived with Olaf, and it was possible that he had recruited them. (The passage in WCTBATH about saving up your fear is relevant to his general character, I think.)
I think Hector may well just have been very skittish about his own hidden past - though it's also likely true that he would have been under orders never to reveal his V.F.D. connections to anyone, at least not before recruiting them. Does he ever actually lie about his past, rather than just leaving things out? Still, just think what the poor man must have gone through when he saw what was happening to Jacques, though!