1. The smoke:
Yes, do change the oil to 15w40. Any chance it is over full or contaminated with gas?
Were the cylinders oiled prior to storage or before it was started? Possibly it's just residual oil in the exhaust.
If it was stuck, chances are the rings are stuck. They rarely free up on their own. Sorry...
2. The carburetor:
The small screw id the idle mixture screw. Turning it in richens the mix, out leans it. It actually adjusts air bleed, not fuel, so it's backward of modern carbs.
The idle must be down around 400-500 RPM. Any higher and the adjustment will have no effect. Back it out to rough idle, then back in to best idle. It has minimal effect, so the adjustment is limited.
The large screw is the main mix adjust. Turning the screw in leans it, out richens it. Start about 2 turns off the seat.
To adjust it, idle the engine down, then suddenly goose the throttle, observe the response. Turn the screw in 1/4 turn, repeat the test. Keep doing this, 1/4 turn in at a time until the engine falters on quick throttle. Then start backing the screw out 1/4 turn at a time until the engine takes full quick throttle from idle without balking. A single puff of black smoke is desirable.
But, the carb adjustment should be the last thing you do. The carb will only function as well as the rest of the engine. If the ignition is right, air cleaner serviced, thermostat working, compression good, valves adjusted, only then can the carb be successfully adjusted.
3. The throttle:
Sounds like either there is a governor problem, or the throttle linkage is out of adjustment.
Start with the engine off. Set the dash lever to idle. The carb throttle arm should be held tightly against the idle stop screw. Then set the dash lever to fast. The carb throttle arm should be spring loaded to the full open position.
Next, disconnect the throttle control rod (the link from the governor arm to the carb) by pulling the pin from the rod clevis.
Set the dash lever to a mid position. Hold the disconnected rod with your left hand rearward, hold the governor link gently to the forward position. You are now in control of the engine speed, so be careful. You right hand is also close to the belt, so be extra careful!
Have an assistant start the engine. Gently bring the engine RPM up. As the RPM comes up, you should feel the governor arm begin to push back. Don't hold it, let it do what it wants to do, just hold slight forward pressure. Continue to bring the RPM up until the governor arm reaches it's full rearward travel, note the position where it stops.
Shut off the engine. Now adjust the length of the carb rod by screwing the clevis in or out on the rod so the length equals the noted position of the governor arm at it's rearward position, with the carb against the idle stop.
See what happens here? The governor spring wants to pull the carb wide open, while the spinning weights try to push it back closed. The faster the engine, the harder the weights push back. Engine slows down, the spring opens the throttle more. It's a balancing act.
Now, if you did not feel steady push back on the governor arm, there is a problem with the governor. The governor is behind the timing cover, and they do have a reputation for failing. The ball cage will break, letting pieces of the cage fall into the oil pan, and run through the timing and oil pump gears. Not good! If it is broken, the governor will not function.
But if the governor is working, and the adjustment was successful, you should now have smooth throttle response. To make the final governed speed adjustment, set the dash lever to full speed, loosen the U bolt above the generator, rotate the spring lever to get 2000 RPM on the engine.
Sounds confusing, but once you get in there it's not. You can find more instructions and a diagram online. Search "TO35 governor adjust".
4. The prominent miss:
Could be lots of things. Have you run a compression test?
Do revisit the distributor. The shaft bearing must be tight, Any side play and the points will not stay set. Be sire the centrifugal advance is working. The rotor should turn a few degrees CCW, then spring back when released. If it's frozen, or slow to spring back, the distributor will need to come out, be taken apart and repaired.
Check the valve train, look for broken valve springs, check the valve clearance. While the tank is off, be a good time to rinse it out.
Check the air cleaner. There is a wire mesh inside the canister that is often overlooked. It must be periodically cleaned, not an easy job, but needs to be done.
Hope this helps, let us know...