Welcome to vintage restoration. Your bike is made out of pure unobtainium.
Actually it isn't that bad, but it is that slow. I took the liberty of searching eBay for you and there are several PE parts including a carburetor selling right now. I just searched Suzuki PE so you will have to refine the search.
What may happen from time to time is you will wait weeks for a part to become available and be outbid by some last second bidder. Just the way things work.
On my Suzuki the frame numbers are stamped on the steering head under where the headlight would go.
Rick