Can you burn fate points to revive yourself if you get a 100 in perils of the warp as a psyker? It might be mentioned somewhere but I can't find it.

Yes, with GM approval, because: "The result is that the character survives whatever it was that would have killed him, but only just." and "In more extreme circumstances ... it is up to the player and the GM to work out just how the Battle-Brother makes his escape"

Corebook, p.205

Burn to survive, yes, that should be possible. Or at least, until the GM says "no."

What I would say is RAW though, is that Fate Points can't be used to re-roll Psychic Phenomena/Perils rolls (I do note that you're not asking that here, but I feel its a meaningful aside in this discussion). Fate Point re-rolls are for Tests, and Phenomena/Perils rolls are not Tests.

It wasn't adressed in DW, but in Only War errata it's stated that psyker can use Fate Point to reroll Psychic Phenomena even after using "Favoured of the Warp" (OW Errata p.37) DW Librarians are far more powerful than IG Sanctioned Psykers, so I think they must be allowed to do the same trick.

Wow, didn't realize a change like that was put into the OW errata. Then again, I shouldn't be surprised, these are the people that decided Overwatch should be able to perform an infinite number of attacks in DH2e.

As a GM, I would call BS on that "clarification." Its a bad call and takes what should be a brutal aspect of the system and trivializes it. Still, as it stands with DW, Fate Points are to be used with Tests, and again, as currently written (and at least now they're not gonna be writing more) Psychic Phenomena/Perils are not Tests.

DW Librarians get they ability to re-roll Phenomena only at Rank 4 for Warp Conduit (1d5 Corruption points for every use, ha) and at Rank 7 (!) for Favoured by the Warp. I don't think that allowing re-roll for Fate Points will weaken the brutality of Psychic Powers system.

But it up to each table, as always.