Very, very, very partial and probably wrong answer
(I normally wouldn't post anything so fragmentary, but this has been sitting unaddressed for three weeks now.)
2; The odor of the weasel protects you.
Well,
according to Pliny, "the odor of the weasel" is the only weakness of the basilisk. Now, where have we seen a basilisk alongside the number 2? One candidate would be the second of J K Rowling's "Harry Potter" books, in which a basilisk (as it eventually turns out to be) features prominently.
So perhaps
the other number/phrase pairs indicate other dangers or adversaries in appropriately-numbered Harry Potter books? Though the fact that there are seven of these and six faces on a cube is not a good omen.
Unfortunately the only other match I've been able to find is extremely tenuous:
4; 15 down, 53 right, add 92.8 in all of Hastelloy's might.
It occurs to me that
perhaps 92.8 is not a single number with a decimal point in it but the numbers 92,8 signifying the elements uranium and oxygen, or more precisely their symbols O and U. Hastelloy is a brand name for various corrosion-resistant metal alloys; if we suppose (as is in fact the case) that some of them include chromium and carbon and insert OU between Cr and C, we almost get CROUCH, the surname of a key Bad Guy in the fourth book. But I don't see where the H is coming from, and I haven't been able to make "15 down, 53 right" turn into BARTY, his first name, even though the R/RT is kinda promising. (The obvious thing to try is looking things up in the periodic table and moving somehow in the given directions, but I can't get it to work.)
Scattered thoughts on the others:
1; Gorgon of three.
Well,
#1's title makes reference to the Philosopher's (or, if you're in the USA, regrettably the Sorceror's) stone, but that seems super-tenuous. And apparently (though I hadn't remembered) Hagrid exclaims "Gallopin' Gorgons!" at some point in that book. None of this seems very useful. The gorgons' names were Stheno, Euryale and Medusa, but that isn't helping me either.
7; Cube, then add back.
No good ideas on this one.
#7 is HP & the Deathly Hallows. Really the only key adversary in this one, so far as I recall, is Voldemort; maybe you could add Bellatrix Lestrange? Lucius Malfoy? Horcruxes? Snatchers? Fenrir Greyback at least has a name ending with "back", but bleh. If we interpret the words mathematically, perhaps we're supposed to take a cube, reverse its digits, and add the results. That gets us 2 16 99 110 646 828 686 727, none of which rings any bells whether or not this Harry Potter idea leads anywhere. (Or we could e.g. take 512, 512215, 5/12/2/15, ELBO ... but I don't recall elbows featuring prominently :-).)
The "two hieroglyphs"
are a large Greek letter chi rendered in Microsoft's hideous Symbol font, and a logo of Texas Southern University. If there's a connection between either of those and any of the remaining 3 books, I'm not seeing it. TSU has a "Tiger Walk"; perhaps whoever pressed that face got eaten by a tiger?
One variation on the theme above:
perhaps each of our four inscriptions pertains to a different series of books