Yes you can drive a snowmobile in Canada with your G1 as long as you are insured, you can not drive on the 400 highway but who would anyway with a snowmobile, but you can ride the OFSC Trails as long as you have a trail permit and sticker as well as plate and insurance.
The drive belt is fixed. There is no way to tighten it. They are model specific. You need to have the correct belt for the snowmobile. Now if you are referring to the track, that would be a different story. They are adjustable.
There are no snowmobile licensing requirements for anyone born before January 1, 1977. You can contact the following for questions about snowmobile safety in Minnesota: Snowmobile Safety Training Program Headquarters Camp Ripley, Little Falls, MN: 1-800-366-8917