This thread should be renamed to "Why is Flandre in the basement" or something like that.
Anyways, I recommend going back and reading all the actual official works/dialogues that involves Flandre. It shouldn't be too hard because there are only like, two and a half of them (her conversations in EoSD, her Bohemian Archive in Japanese Red Interview, and her EoSD profile. Feel free to read her PMiSS article too, if you want to, but that one's largely just a reiteration of things you should already know combined with a bunch of "well duh" speculations by Akyu)
As far as I can tell from these things:
1. Flandre is actually very mature sometimes, as far as I can tell. She's incredibly coherent in the three dialogues she's involved in (EoSD's dialogue with Reimu, dialogue with Marisa, and BoJR) and if anything, she's sometimes possibly even more mature than Remilia if she isn't lying when she talks about her in BoJR (where Flandre comments that Remilia overexaggerates the control of her fate changing abilities). Although on a grander scale, Remilia's probably more mature (since Flandre just sticks to the basement while Remilia will actively get involved in or at least consider the bigger picture if needed, as shown in IN, IaMP, and SWR)
She is described however as "emotionally unstable". We never actually see the full extent of this in any of the three dialogues she's involved in, though (although depending on how you look at things, there might be some small subtexts and implications of it in her extra stage dialogues here and there). Presumably it manifests in how she just tends to get carried away sometimes (like when she tries to eat a human, as mentioned in PMiSS. That's the only example of emotional instability I've ever seen regarding Flandre, really, but it is admittingly enough to show why Remilia would want to keep Flandre locked up)
2. Flandre might have never left the basement in hundreds of years, but she's still exposed to "outer stimuli" because she has some amount of Omniscience (the ability to know everything). We don't know the exact range and extent of this Omniscience, but she can clearly SEE beyond the basement. She saw the entire events of EoSD from the moment the heroines entered the mansion (possibly sooner) despite being in the basement the whole time (her dialogues in EoSD). It's possible her ability to view things extends into outerspace and beyond, since she was able to see the eye of the meteor. In fact, the way her power works is that she can see the eye of anything as if it were in the palm of her hand. This is probably where her omniscience comes from, although again, we don't know the full range of it. This is lampshaded by PMiSS, where Akyu specificaly states that the range of her power is unknown. It's possible that Flandre can see almost EVERYTHING in order to be able to see the eye of everything. At the very least, we know that her ability to see the eye of things extends into orbit, and thus likely her omniscience has this amount of range as well.
...at any rate, she is clearly able to see outside stimuli. For whatever reason, she chooses to not go out and interact with it most of the time (however, it is likely she's tried to go out before, considering that Patchouli already knows what to do whenever Flandre wants to go out. See point 4.
3. Combining the two above points, Flandre must be pretty naive. She has lots of omniscience and saw what was going on in the Scarlet Devil Mansion, yet says she never saw humans before. She doesn't even know she's eating humans according to her official profile. Does she even know that Sakuya is human? Well, it's possible that her omniscience works in such a way that it's hard for her to identify such details, especially if it primarily works mostly just by her seeing the eye of things, in which case, the version of EoSD's events that she saw must have seemed like some strange acid trip. ....actually, if the entire world and everything else by her gets viewed in some strange psychedelic "eye of things" way, this might explain her unstable personality and insanity.
4. Flandre is "locked up" in the basement, but can easily get out whenever she wants to. This is shown in the storyline of the Extra stage, where she easily just comes on out because she wants to go to the Hakurei Shrine too. This is likely something that doesn't happen very often. It's probably a decent enough assumption that this exception occurred because Reimu is special (storyline-wise, Reimu has this sort of effect on people. Check out Koichi's official prologue for example)
It's not particularly disastrous whenever this happens. At least, Remilia doesn't appear to be very worried in the Extra stage's backstory. Poor Patchouli is a bit freaked out, though, but that's probably because she's the one tasked to keeping Flandre inside while Remilia and Sakuya are away.
Patchouli contains Flandre by making it rain, by the way. For all of Flandre's power, she still has the typical vampire weaknesses and thus can't leave the mansion as long as Patchouli is making it rain. It does not appear that Flandre is aware that Patchouli is the one doing this (in her Extra stage dialogue, Flandre is dissappointed that it's raining so she can't go out after all but doesn't mention Patchouli, so she's probably unaware that Patchouli is the one causing the rain)
5. For what it's worth, in IN, Remilia is considering getting Flandre a tutor. Course, maybe she's just joking since at 495 years, it's a bit late for THAT.
