potential spoilers:
starting with the Nameless, it's not because we are resistant to his powers that he doesn't control us. it's because he can't use them in the temple due to it being protected against him. and the reason we aren't going insane from even a single gulp is prolly because the nameless made the curse SPECIFICALLY for the lizard people, not humans. from what I've read in game I believe the curse just forces out deep desire/puts a person into a far more feral state which why they go mad. since the lizard folk are beastkin, it might be like a heat state some animals go into where they desperately want to do stuff and have kids, but instead it's just the lizard folk wanna fuck anything to relieve themselves and go mad in the search for it. also, he does say he wants us to willingly serve him, but he can control us if he wishes. he literally forces us to thank him in the nightmare where he killed Rhot and made us relieved after we throw him the gem at our home, showing he did have a slight part of us wanting to give it to him at that moment. also, I'm pretty sure he doesn't stop us because he simply doesn't care, if we resist him, it's no big deal to him since all we did was stop one of his plans and in the end, we still gave him what he wanted. also even with the witch's aid, he still can control our friends, just not us in particular anymore. and from what I remember about siding with her he tells us to leave him alone and he'll leave us alone. maybe I'm misremembering something though since it's been a long time since I last sided with her because I find nameless way to hot lmao.
no idea about Viccoria. she is one of the people in game who has less content than I have braincells so like, idk if she was telling the truth lmao.
but basically, everything else, I think has a really good basis to believe! we know absolutely NOTHING about our characters past, making in all honesty anything possible. not everything is reasonable, but what you've suggested all has a base in the game for being possible!
(on the point below, after going through the intro to check a small thing, it seems like we might have found him randomly instead of him just taking us in. might have misread it a bit though. still think this idea has a good base!)
such as being inhuman, the point on us just appearing suddenly and becoming an apprentice doesn't feel likely and our strangely insane constitution against diseases really make us seem more suspicious of being non human. it could be just a gameplay thing because Hyao knows it would prolly be REALLY annoying if we literally HAD to craft a cure before a timer so he left it as a plot hole for the sake of not making us suffer. but off that and on what we might be, the teacher did have notes on lycans in his stuff, so maybe the reason we know nothing about ourselves is because we are a cured werewolf our master took in after curing and a side effect of the "true cure" is amnesia? maybe the quest/place/whatever the master is doing is going to a place infested with Lycans and he is going to save the people and cure the Lycans, which would also explain why his notes never had a cure. not because he couldn't but because he took those notes with him! this one is mostly pure speculation though since our character would prolly notice if notes were missing unless the teacher happened to have like 2 copies one of which was finished and one which was the original but never got completed.
the Wererat idea though I severely doubt. I'm pretty sure they aren't created via humans being infected but are born of a mother and father ratkin. however, I don't have any proof for or against this, just that it seems unlikely to me. plus, if they were created via infection, that means Scrap was once human and he would prolly remember that and his story wouldn't be "embrace the whore rat" or "act more human" and instead be "embrace the whore rat" or "remember your old self". so only the route about being more human like would really change.... but still, point stands. and the wererats would prolly have caused our MC more concern if they could infect people since they were so close to the town and could infect everyone. but the resistance to spectral fever is something I don't understand at all. maybe they had a plague and eventually evolved into a resistance to it? or it could be a not a disease to them and only to us? maybe it's being inhuman which gives the resistance? which would in a sorta funny way add credence to us being inhuman as well lol. hope we find out why they are resistant to it so we theorize about ourselves.
also how long we had been with the master was stated in the beginning, just a couple months. it's literally ONLY mentioned in the intro from what I remember though so it seems really easy to miss.
but off us being a werewolf or such, what else could we be if not human? maybe a homunculus? we don't know if those exist in this world and if they do it could explain some stuff about us. such as the strength increases passively with nearly no limit and how we stayed with our master. maybe we think we found the teacher, but he actually created us and the reason he left was to deal with rumors/the consequences of our creation? or someone else made us and he realized what we are and took us in to protect us until we could protect ourselves from others who would seek to use our power.
I would say demon or something similar but we meet Viccoria and she would absolutely notice if we were a demon or such, plus it would appear demons are weakened by sunlight and we are completely unaffected by it so I highly doubt this idea. maybe I'm missing something though.
another idea though could be a sort of Fae creature? like how Feliar is a Satyr we might be some sort of... I don't actually have anything since all the Fae creatures I know have major visual identifications like fairies with wings and Satyrs with the goatlike features. but if anyone has a creature humanlike please share it!
maybe we are human, but a human who was experimented on and eventually discarded as a failed product and we don't remember it because we just got into an accident or something and met the master? or we are aware of it and remember but hide it from everyone and it just hasn't come into lore yet so it's not been mentioned?
and again, even if a stretch, really fun ideas! so long as your enjoying it I bet Hyao is happy about this :) and I also like thinking about possibilities in the future of the game, but you had some ideas I don't think I could ever come up with on my own lmao. even without a good amount of evidence, they have just about enough stuff to make them mostly possible! I hope we find at least one thing about ourselves so we can confirm/deconfirm our theories and stuff.