I have a question about why both my pokemon x game and pokemon y game will no longer allow me to connect to my router (for both the wonder gift torchic and for GTS), but I am not sure if technical-issues can apply to problems with routers, or with handhelds, because it seems to mostly be about actual bugs with a game itself, usually on a computer. I can't ask it on super user either, because they have no 3DS tag and I doubt they would appreciate questions that do not apply to computers themselves. Can I ask tech issue questions about a 3DS and a router here, even though it does not relate directly to the game?
Yes you may. Connecting a gaming device to a network falls under Game-specific hardware and utilities. As you've pointed out, the people at SuperUser may not know what settings to check on a 3DS, while people here will.
The technical-issues tag is not required. All the other questions we have regarding gaming devices and routers are simply tagged with the device in question.