Ok so beware of the big wall of text incoming
Whodunnit: Frank
Whydunnit:
William's card said "The sun's light falls upon all of us equally" "Soar too high and you will burn". It seems the culprit is punishing and blackmailing the abbots for their corrupt business of demon hunting (like Pongy said in the post above).
The culprit was also possibly getting groomed by William and he ended up finding out about that secret business of them through this relationship.
There's some weird thing going on between the temple of Noch and Smed, why do all of the monks that end up going there (the ones we know so far) have a story of being converted into werewolves, vampires or being groomed into becoming one (Remigio)? How did Frank get here in the first place if they were interested in Aloys in the first place? I think all of this is pointing that there are things we don't know about Frank's application for the church of Smed. The story tells us at some point that (besides Remigio) Aloys and Frank are the only Noch monks working there.
I also want to mention that the scene where they are luring Lucusti out with Alessia's catnip-poison-thingy made Frank very suspicious IMO. We are there expecting for Lucusti to appear but we get a very curious Frank first. It made me think of the possibility of Frank being a undercover descendant? I don't really know how far could their powers go or if they have similar powers to shapeshifters. We could also assume the possibility of someone being half-descendant? Maybe he found a hard truth that he didn't want to know?
Howdunnit:
I don't believe that Santiago lost his keys before Giorgio's murder. I can totally picture that he's still lying to make his mistake less severe. As we've seen so far he's clearly someone very proud and grumpy. He knew there was possibly a murder crime going on but he'd rather play dumb instead of acknowledging that he lost his master keys and taint his image. At the moment of Giorgio's dead he had no other choice but to confess that his keys were stolen, but he lies about the moment he lost them to avoid making it seem like a bigger issue. There's no reason for Santiago to commit the murders as we saw that the abbot's inner-circle doesn't want their past secrets revealed and they fear that this information comes out somehow once William is death (Especially with those documents going around).
Even if Santiago lost his keys right before Giorgio's dead, it is still possible to commit the first murder if the whole "Frank getting groomed by William" thing is true as he'd have a way to get into his room for the first murder anyways.
So with that aside. It'd go like this:
Santiago has the habit of lending his keys to Remigio because they are friends. At some point Frank stole the keys from Remigio or found an excuse to make Aloys steal them. This way Frank has easy access to most rooms where the murders are committed. Santiago and Remigio were hiding the fact that those keys were lost.
1st murder:
Since Frank is getting groomed by William, he went into his room and when William gave him his back he striked. Then he started the fire, went back to his room with Aloys (who was already sleeping so didn't notice him arriving) and pretended he never left in the first place. Then they got called into helping with the fire and he made sure with his own water abilities to avoid the church getting burned (which has William's study). This last bit would be important in the next murder.
I want to mention it is important the fact that the first murder had a fire started. Only the culprit that knows he could avoid excess damage with his own water abilities would think that starting a fire is a good idea.
2nd murder:
Frank stole the church keys at Amelia's office when her apprentice was out. He took two to make the illusion of the culprit not having the master keys. Since he knows he has Santiago's master keys and he knows that he'd rather not say he lost them, he makes use of this to broaden the suspects. He sent one of the documents along with a church key to Giorgio, this would imply that there were more there and that if he wanted to get rid of them he'd have to go get them himself.
The night Giorgio died he went to Brandeis cell first to discuss the issue and he possibly gave him the document he received (this is why this was never found). Then went to his cell and pretended to go sleep. None of the hunters saw him leave his room, as stated by Leila, because Giorgio left through the window. Then he got into the church with the key he got sent and since it was dark, he got killed without possibly knowing who the culprit was. Frank had an encounter with Bitey but managed to escape without revealing his identity.
3rd murder:
Ok so for this one the whole book thing is important and the window clues are there to deceive us into thinking Remigio could easily be the culprit (especially if you sum the whole Santiago's stolen keys thing). We know Frank spends a lot of time in the library and that he also works at the scriptorium, so he could be the person who prepared the books. Out of all the characters presented in the story the only two we know work at the scriptorium are Aloys and Frank. The culprit purposely gave Leila 5 instead of the 6 requested so he then had an excuse to go there himself with the extra book. Once there, since Oscar was possibly distracted reading his book, he simply asked to put the 6th book on his desk or something while ignoring Frank and that's how he got easily killed. Then Frank set up the scene to make it seem someone entered through the window and then he left through the door. Since Frank's appearance isn't weird for the hunters, and they found Oscar dead with the window open and with all the fake clues, they didn’t suspect Frank.
Of course I think if the detectives get to interrogate the hunters that were guarding Oscar better in 0.5 all of this could change. The only information we got was from Bernando and Leila.
I may reply to this message later to add some extra points that made me think why Frank could be the culprit or at the very least an important accomplice.