I had to do some reading, and I learned a thing, but I think I've got it.
According to page 124 of Realm of Power: Infernal:
...while he may learn magical Supernatural Abilities, because of his association with the Infernal realm these are actually False Powers that always appear unholy to Divine or Infernal Powers of investigation
And according to page 36 of the core book:
The ability to cast Hermetic magic is the single Supernatural Ability possessed by Hermetic magi in virtue of The Gift; again, they may take more Supernatural Ability Virtues if they wish.
I didn't know that Hermetic Magic was just one big mondo supernatural ability, but there you go. I think that, given these parameters, everything you do with the False Gift is infernally tainted (covering your first and third question) - except, perhaps, for your second question (about lab texts).
Given page 101 and 102 in the core book about Lab Texts, it seems as if each magum invents each spell they learn, and lab texts are only guidelines that speed the process. The magic isn't learned directly from the text, and so the fact that one version of the spell is infernal because it follows from an infernal Gift, does not require that spells invented by non-infernally Gifted individuals also be infernal.