The drive belt should run fairly much on the sprockets if they have guide plates on both inner and outer faces, front and rear. Not easy to achieve but it can be done, a straight edge along the sprocket faces helps a lot when setting this and the bevel box and/or swing arm may need adjustment to get it all in line.
Early cars didn't have the belt guide plate on the rear wheel sprocket outer face but they also had a different spacing for the sprocket on the rear hub, silver hubs, later cars had a black hub with different offsets. If you have the early set up then the belt will run about 3 or 4mm off the outer edge when set up correctly.
For later cars the guide plates should be just that, guides, not restraining plates. Once aligned and tensioned correctly the belt should stay within the guide plates without any excessive side loads. You should also have about 3mm clearance between the belt and the tyre sidewall, although some tyre brands are a bit "fat".
I can only assume that the belt touching the "frame crossmember" is the chassis tube that is under and slightly aft of the bevel box pulley lower run? That is usually because the tension is too low and the bottom side of the slack belt "grows" with speed and increased load as tension is put on the top run and the slack is on the lower run and rubs on the tube, sounding like a turbine.
The drive belt is usually bullet proof and hard to damage. When correctly set up it requires just the occasional clean with soapy water to keep it working perfectly and lasting thousands of miles.
