Yeah idk where everyone is.. I like new project threads.
The frame is probably quite sturdy enough. Hard to tell the guage (wall thickness) of the metal from a photo, but age and being made as transport rather than racing makes me think it will be fine. The wheelbase is long so should help it to be stable at motorised speeds. The bend in the fork will absorb some high frequency road bumps so that your hands don't tire. It is taller than necessary as you are not going to be pedalling.. But idk if that would be a problem. It's forward slanted rear dropouts should be good for getting the correct chain tension with less fuss. I quite like it in a lot of ways.
Yes you should be able to weld that frame as it is steel, unlikely to be any kind of special heat treated or whatever, just high tensile steel. It really needs tig welding or brazing (I think I can see in the photo it has the sleeves at the joints because it is brazed, not welded). I had someone MIG weld a bike frame repair for me once and though it worked it was not pretty by the time he finished filling the holes back in that he burned in it! I hope you would look into getting the mounts for v brakes if you are going to modify the frame.
I never read about brazes failing due to vibrations, and it has survived this long, I think it is really okay as it is apart from the old style caliper brakes.
You should still think about making some modifications to your engine to reduce vibration for better comfort (and the health of the engine at higher engine speeds) anyway.
Frames built to take wider tyres generally have more clearance to get the motor chain through.. They can have a straighter return (lower) side of the chain, which means less strain on the idler pulley when you bump start the engine.
It looks like the rear wheel has already been replaced, that is good. Spokes should be stainless steel (shiny) not cheap wire (grey).
The tyres look like maybe 622x32mm which is fast and economic, but they (32mm) are the size I use on my touring bicycles, on roads and being careful and pumped up to 70/80psi, but loaded up with a lot of weight.
I think there's a happy medium on the tyre size you actually use, but that depends on your weight, your roads, your riding style.. 622x47mm might be preferable for motorising if there are unavoidable bumps in the roads, but only you can know that. You might need a 3" tyre mountain bike to protect the rims and your spine but it would get many less miles from the tank of fuel- what suits you will depend how you ride and where!