Good summary of the salient points.
1.
Ebay (and other places) show up a host of suppliers of bolt on 80cc engines.
@Coxsy hull , you'll fall foul of Construction and Use regs at the very least if you want to use it in public. And then it will become a moped/motor bike, so will need insurance, VED etc. This isn't something the various sellers bring much attention to, as all they want to do is relieve you of your hard earned money.
2. I'd be wary of stockists giving unbiased advice.
3. Can't help on the making you get off and walk in a pedestrian precinct I'm afraid. From the outside it does sound like Humberside Police might be overstepping the mark, but on the other hand even your electric conversion is subject to various laws, regardless of how good a job your mate Chris did on it, so you may have to act a little carefully.
Sorry I can't be much more help.