do you think that light yagami actually cared or felt bad that he killed a human being? or only freaked out because it so strongly contradicted his character?
also why do you think light puts on this incredibly rigid and perfectionist facade when others like him, L near mello naomi, dont? why is light sensitive to rejection
0. in love with the fact that you included naomi in 'others like him' SO true
1. i haven't reread ch1 in a while so take this with salt but my general impression is that for manga light it's both - like his nausea after killing shibuimaru is about it contradicting his character ("i killed two people... me...") (italics mine) and i would say that is the defining characteristic of his immediate subsequent decision to double down and make it not contradictory to his character after all, BUT i do still think he cared about killing A Human Being. it's not connected to any of the human beings he kills specifically, but his monologue while in his blanket burrito is
(this is from my fanslation lmao but iirc the viz is pretty much the same. it's especially interesting that this is after he gets home from killing shibuimaru - "just two, and look at me..." - like, he had that whole dramatic moment where he decided to Clean Up The World prior to this and then he goes to his room and still has a breakdown!)
and of course much later, while talking to matsuda after soichiro's death, he says somberly that kira probably thinks that what kira is doing is evil but it's worth it.
that said i don't think he feels bad for anyone he killed in specific - we never see him feel anything for the inner lives of criminals/"immoral people" and he enjoys it when it comes to people who specifically wanted to get in his way (raye, naomi, L, etc.). you could interpret this as a corruption arc but considering how that stuff about what kira is doing is evil comes much after this, and how yotsuba arc light says that kira's killings are "frighteningly close to [his] ideals" but he doesn't think he would become a murderer himself, i don't think it's a corruption arc so much as a disconnect between the concept of killing a person (bad) and the act of killing a person (yay). if that makes. any sense.
ANYWAY all this to say yes i do think he freaked out because he cared about/felt bad for killing a human being and because it contradicted his character, but i don't think he freaked out because he felt bad about killing kuro otoharada and takuo shibuimaru. his torment about killing is very generalized. your mileage may vary though.
2. why do you think light puts on this incredibly rigid and perfectionist facade when others like him, L near mello naomi, dont? why is light sensitive to rejection
my kneejerk instinct is to say that is just How The Character Is but if you're asking what factors influenced it, then probably the fact that he is breezing through the education system but is also stuck in place (skipping grades isn't nearly as much of a thing in japan) and his mom and sister are both very quick to praise him BUT his father is somewhat distant due to job reasons BUT ALSO has enough confidence in light to tell him about investigation details such that light has solved two cases for the npa before canon even starts, so it's kind of a perfect storm for 1. receiving enough support (and affirmation of his identity as Top Student) that rejection (and negation of his identity) comes as a shock; 2. a craving for approval, nevertheless, so the rejection actually hurts; 3. a belief that there is always a way to get that approval somehow, so [gestures at everything he does to get it]
the others are all missing a few of these elements: naomi doesn't get much praise from the department (according to labb) and raye puts her down constantly despite possibly not meaning to; we don't know enough about L's backstory to say but certainly interpol doesn't seem to like him very much; mello is constantly second place to the point where he just straight up gives up the successor title to near so he can prove himself a different way; and near isn't ever in a position to get approval from anyone who really matters.
the closest to share this particular complex of light's might actually be misa, though of course it manifests very differently - she's used to her charm working on people (e.g. her exploiting her occult friend effortlessly) but she is desperate for approval from kira who it doesn't work on, and so she spends the entire story scraping for more and more crumbs.