If you're staying here only a few weeks, don't you have some sort of itinerary planned? That would tend to take care of meeting people. Otherwise, what are you doing during the day -- attending classes? (another route)
As for being gay, it's moderately open here. More of a novelty, but I don't think there is half the stigma attached to it as elsewhere. I don't think it's likely to come up in such a short time, so if you want to keep it a secret, that's your prerogative.
As for getting along with fellow teens, just be yourself, but keep in mind that there may be differences in some cultural things. Go with the flow. Teens are teens (although I have found as a teacher in HS a few years, that J teens are often lower in maturity levels). Expect things like Disney characters or cartoon characters on their phone straps, for example. Everything foreign is labeled "cute". Most of all, don't expect anyone other than the very bold to make any first moves in approaching you to say hello most of the time. They are simply afraid of being unable to communicate, that's all. Be open and inviting and do your best to stumble through what little Japanese you know, just to show them it's ok to make mistakes.