I honestly never expected anyone could overanalyse a manga full of feels and sugar to this extent. I don't mind saying that Santa is probably my favourite ongoing comic, so I might be a bit defensive of it. That said, your so-called sound points still look like exaggerations to me.
Something would have to be giving Cookie these ideas.
1. Romantic relationship distinct from a regular one.
2. That friendship is antithesis to romantic relationship
3. Concepts of monogamy and jealousy, at least at his level of jealousy.
3. Monogamy just sounds plain ridiculous at his age. Jealousy, perhaps but it's the kind of jealousy children have (like what my 7-year cousin would feel when his parents dote on his baby brother). I don't find that annoying. Also relevant: the point where you mention he's crazy possessive and doesn't act like a 7-year old. Well, I think he does, children are possessive!
If the author doesn't explain how Cookie got these ideas and expects us to believe that Cookie came to these ideas on his own, and if the author doesn't have someone set Cookie straight, I will be very angry and disappointed. Already some signs of this when the author has Bell understand what Cookie is driving at when he confesses to her and that "her heart beats faster" and shit.
Bell helped him find his magic wand when they first met, she's the only one who's the same age as him so they can most likely relate to each other best, she's well-mannered, and helpful. They often read books together, they've been staying in the same household for a while now. I don't see why it's unusual for Cookie to get ideas that he likes Bell. His feelings were made obvious a long time before he confessed.
Really Cookie is being completely unfair to Bell. What he is imposing on her is the preamble for sexual relationship, and whatever age they are, they are clearly too young for that. So instead he's putting unnecessary labels on their friendship, and jeopardizing it. He is also acting crazy possessive, unlike any 7 year or whatever age should act like. It's unhealthy for both of them I think.
Uh what? Preamble for a sexual relationship?
I believe there's nothing wrong with finding one friend more special than the rest and wanting to be with them more often. That doesn't jeopardise your friendship; it's more likely to strengthen it. There was one occasion when Cookie was close to being possessive, and that was when Bell was talking to Healer right before he confessed. I just read some chapters again and couldn't find another instance where he positively tried to stop Bell from being with/talking to someone else.
Oh, and how come they notice that one girls pointed ears, but don't notice how Bell and Cookie have Christmas tree ornaments for eyes. Well often in these comics people are drawn like mutant freaks but christmas tree ornament eyes is a whole new level of obvious freakishness that's treated like normal.
Everyone's supposed to have a unique eye but that's not really the case with ears, so someone whose ear is different is more likely to stand out, right? And uh... it's the author's own fantasy world, so there's nothing wrong and most definitely nothing freakish about giving each person a unique set of eyes. I personally liked them and judging by some comments, so did a few others; too bad you didn't.
tl;dr: Many children are possessive about things, get jealous quickly, and are quite often sore losers. They do not actively mean harm though. We still find them cute, and they grow out of that phase at some point.