That should be easy enough to connect it to the fuse box, the current draw will be low so need to start uprating fuses etc if you connect it to the side of a fuse holder which is dead when you pull the fuse out.
Extend the wire from the head unit if you need to, as long as the extended wire is the same the diameter or thicker (The wire core itself).
You obviously to need to find a fuse in the fuse box which is live preferably when you have the key turned to the accessory position so you can use your head unit when parked up . I don't think the air conditioning fuse would be live unless the engine was running, unless your happy to just use the head unit when the engine is running of course.
It's always useful to have a multi meter for identifying ignition live feeds etc , there should be one in the fuse box I would think.