I can help you out on the running Jack.
Personally, I would avoid running every day, if you aren't specifically training to run, I would say 3 runs a week would be sufficient, I would break these down as a short (3 miles max) steady run, a longer tempo or speed session, and a long slow(er) run at the weekend.
That way, you aren't putting excess strain on your joints, the tempo / speed session will improve your "twitch" muscle fibres, which would help with karting, and the long run would improve your stamina no end.
On days you aren't running, I would say anything low impact, like swimming, x training, rowing etc etc, even walking, is good.
Personally, I would stay away from heavy weights, because all you'll end up doing is bulking up, which if you are karting you don't want to do, plus it makes any cardio work harder.
If you want anymore indepth info about running (I can help out of running schedules, tempo / speed sessions, pacing, distances etc etc), give me a PM.
Remember, REST DAYS ARE IMPORTANT, you will injury yourself otherwise.