Let's address these in what I think is the order of importance: Smoking.. how long has it run? Depending on how the engine was stored and how long it's run. I had one that was involved in a rollover and there was enough oil in the top end that it it smoked for 45 min in the driveway and then another 20 around town. Kept getting better the longer it ran. If it's getting better as it runs more.. let it run.
The electrical issues: you have a ground or positive wire loose etc. At the transmission where the main battery cable ground hooks up, do you have the battery cable and two small black wires? Because you should. Are all the connections snug at all ends of the battery cables, because the behavior you mention... something is loose.
Don't go into the harness to chase it, it's something you specifically touched and just retrace the main power cables, you'll find it.