First of all welcome to the Kumoricon community!
And firstly, you have absolutely nothing to worry about. Kumoricon may have started among college circles, but the past few years have seen it explode with a much younger fan base. So much so, in fact, that I'd say the younger crowd probably outnumbers the more mature crowd (or they at least make themselves more prominently recognized, but that's another story...).
But yeah, so basically, you've got nothing to wrry about as far as attending age goes. You will be in good company. There are a lot of 13-17 year olds just here on the forums, and the number that actually attend Kumoricon is exponentially greater.
And as for attending by yourself, or even attending for just one day, there is nothing wrong with that. The Kumoricon community is so warm and welcoming, I think you will find yourself invited in and greeted rather quickly. The abundance of cosplay, of people who have come together for the love of anime and other shared interests, it makes us a family of sorts, and we do the best to make the con a welcoming and pleasant environment for everyone because of that.
Whether you come for the whole weekend or just one day, you should have no problem making acquaintances and meeting people who are happy to meet you. We're one massive family at Kumoricon, and any new attendees are more often than not a pleasant addition to the family. ^_^
On any given day there will be some lovely events going on, so if you can only come for one day, just check the schedule ahead of time and pick which events you would like to see the most and come on that day. No problem with that, heh.