I have just one thing I really don't understand. Why is Shana so popular ? Ok she's a tsundere, loli-look-like but that doesn't explain all... Am I missing something ?
I think a lot of people in the anime circle are way too quick to drop the "tsundere" label. Honestly, it's almost like every character in anime gets that label if she's not a soft-spoken, submissive, codependent type. I even hear Mikoto and Mio get the same label, but all three are in my opinion completely different characters. Just because Shana (or Mikoto or Mio) has a rough edge doesn't mean there's nothing deeper than the archetype.
In Shana's case, since you asked, I can tell you a bit of why I like her personally. I think it has a lot to do with the atmosphere of Shakugan no Shana itself. I think there is a very distinct aesthetic, between the soundtrack, storytelling, and introspective pacing of the show that really sets the stage to strengthen the characters. In addition to that, I like the concept of a hardened warrior suddenly thrown into a situation where she has to learn about love, having never even heard of the emotion before. The way Shana deals with this inner conflict is not always graceful (enter the "tsundere" label), but given her situation, it's only natural, and to me, that development is fascinating to watch. I was first introduced to Shakugan no Shana during a pivotal growing stage of my life, too, so there's also that added bonus of being able to relate to her conflict (so yeah, some sentimental power, too). She's not written with the intention of being as adorable as possible, but the realness I see within the fiction here adds something that really can't be surpassed easily.