Ah, I should have worded some parts a little differently, but it was clear that you were talking about a storygame. Also only admins can edit posts once someone has responded to them, which is why you can't edit at the moment.
Anyway, keep in mind this'll just be my opinion based on what I have gathered about your idea, so it's up to you to evaluate it to see if you can get something useful from it.
PLOT GRIPES
So, a lot of this will depend on what sort of world you are trying to establish and what not, but here are my attempts at tearing into your setting to see if you can respond (mind you, there is more than one 'correct' response, it is your setting after all!).
Gem Fairies
They were sent to "find people with noble traits", yet you don't mention what the character's noble traits are. Is "lov[ing] sports and art" a noble trait? Is "lik[ing] to make friends and read books" a noble trait? Or what about my favourite (which I'll get back to,) cruelty? That sure is a great noble trait, specially when it matches the power of the gem...
The reason I got caught up on this is because the idea of something larger than everyday life causing young people to suddenly be a lot more important isn't really something unique, and I know that at least at times, there is no real reason that it is kids and teens being chosen to have super powerful magical powers granted upon them. Yes, sometimes the why doesn't matter, but in this case, I can see finding people with noble traits as a pretty valid reason for younger people being selected (as opposed to 'pure of heart' [granted I can imagine this being handled well, but usually it isn't]).
Another questions I will have to pose is why the gems didn't find people in their own world who had noble traits? It seems like there are some good characters who seem to be pretty capable as is, imagine if they had the boosted power from the gems! Now I'm wondering if one person could have got them all... (I'm assuming no)
Back to the gem wielder gone rogue, how'd that happen! I'm sure answers can be given, but right now I just find it weird that gems designed to find noble people would go to someone super cruel AND stay with them, after all the gems are actually fairies, so why can't the thunder fairy go find someone else? Also why was a fairy that turns people into a "Dark Sage" created? Also a thunder fairy is all about sound, I assume? Or is it just called thunder because Thunder Gem sounds cooler than Lightning Gem?
School or World Saving¿
So I can see that the reason for them balancing their lives between two worlds, one more mundane than the other, is to give a neat contrast and be a sort of selling point for the premise. However, my question is how they hop between the two worlds. It is because of the gems I assume, but why are the gems allowing these 'noble' people to ditch saving their world from pure evil to go study algebra!?
My issue here is that if someone is given great power, in the words of Spiderman, they are also given great responsibility. Don't get me wrong, I think school is important and all, but I just find it a bit weird that people who are given power to save a world would still be going to school for half the day. Also I wonder how they'll explain this to their parents, specially the 13 year old (youngest) and 15 year old (shy, something their parents hopefully noticed, so it'd be weird for her to suddenly be spending all her time outside of school 'with friends').
Names
Ah, the age old tradition of using cool popular names for your own characters, nothing wrong with that, but when you think of it as a parent (supposedly in a modern setting) naming their kid after an Ancient Greek character of tragedy, I have to wonder how that happened.
I also wonder if the names hold any significance, but I guess that'll be answered through reading the finished product.
WRITING
Looks good to me, the pacing seems decent and you don't waste time introducing characters, which is great for something that has a large cast. Granted, not much to look at yet, but I'd say you are definitely on the right track. Will be interesting to see how you handle major exposition when it comes up in story (along with choices, always a pretty important aspect of storygames!).
I'd be happy to give more feedback on the writing once you have more actually story related stuff prepared. I will mention now that leaving editing and polishing for later can be a good method, so you shouldn't worry too much about having it be 'perfect' right away, as that is something pretty unrealistic to aim for.
TL;DR
Keep writing! You seem to be doing that already, which is great. I throw quite a few questions your way, so see if you can answer them or dismiss (for yourself), in order to build up a stronger world by having a more concrete idea of it in your head. It is very possible you already have this, in which case I might have wasted a bit of time, but I do enjoy questioning other peoples work.
P.S. I am getting the feeling that what gems turn you into depends on you, otherwise the prophetic dream is even smarter knowing to call Jake Vermilion before knowing what fairy would go to him.
P.P.S. If anything I wrote doesn't quite make sense, call me out on it, I was in a bit of a rush so didn't have time to proofread as much as I would have liked. Hopefully you still get what I am saying, and manage to get something useful out of it. Also, once again, keep writing!