That is certainly a large one-piece flo-jet carburetor, as I thought. It seems to have a good reputation as a carburetor. You can see the idle mixture adjustment screw sticking out of the top, with a spring under it.
Try watching the throttle butterfly when it does its puff-and-misfire: does the throttle move? If it does, the puff of blue smoke is just due to it suddenly working a lot harder, and generating some blowby, which probably blows a bit of oil into the breather hose, which puts it into the air intake. It shouldn't need to do those cycles. A tune-up may help: adjust both the main jet mixture (at high speed) and the idle mixture (at idle) to make it run as well as possible. Clean or replace the spark plug. Check the clearance between the ignition module and the outside of the flywheel, and set it to about 0.012" (thickness of an ordinary visiting card). Check the tappet clearances - intake 0.006", exhaust 0.010", measured with the engine cold. Let's see if it still does tricks when it is in tune.
The manual seems to think your starter-alternator has an integral regulator, and a rated maximum output of 10 Amps. It is not supposed to initiate output unless connected to the 12 Volt battery. If it is the integral regulator type, it connects directly, positive lead to positive battery terminal, negative lead to ground. To test it, connect it with a 12-15 amp fuse and start the engine. Run it slowly at first, measuring the battery terminal voltage. If all is as it should be, the battery voltage should gradually rise to 14-14.2 Volts approximately. How long that takes depends on the state of charge of the battery. If you have an ammeter with a capacity of ten amps or more, you could put it into the positive alternator lead and check that it charges the battery, and that no current flows when the engine is stopped. Do these things carefully - if the alternator does not have an integral regulator after all, or the regulator has failed, it could overload the alternator, which is why you need to start with the engine at low speed. If you accidentally put your meter across the battery while on the Amps range, you will not have a meter any more. You probably know all this.
