I go on with other hints and tips for your other questions.
1) As you have had recently clean the carb and found dirt, I would remove the tank and clean it, petcock and line thoroughly however industrious and hard job that is to make good. Final rinsing can be done hose down with water, just rinse with denatured spirit or ethanol to soak up the last of the water. And then try with a tank of fresh premium gas without any additive. Preferably non ethanol. Or you can run the bike with an auxiliary tank that is clean, just for test purpose.
The engine should run just fine with lowest grade regular, it is just that lowest grade might be slush quality with whatever settlings that the petrol company wants to get rid of.
2) At the base of the breather tube is the rebreather valve, it is just a flat disc that is oscillating back and forth with the air flow that the pistons make when they go up and down. Normal is a pulsating or fluttering sound from the tube.
A wheezing or whistling sound signals that the disc is stuck. That is upsetting the lubrication system and needs fixing without delay. Just remove the tube and clean the seat and disc. No gasket, just a thin smear of (anaerobic) sealer or at the most a very thin paper gasket should be used between the tube and crankcase because the disc can/will hang up in the gap between the housing and crankcase (or cam cover), that the gasket makes. It can be fiddly but a dab of grease will hold the disc in place in the tube seat, at reassembly.
1928-29 engines has a second breather valve disc inside the cam compartment, the housing is different and they don't tend to stick. A gasket there must never be used.
3) Same colour plugs does not rule out ring problems, unequal colour would indicate problems with one cylinder. Today's ethanol blended gas does tend to show much paler/whitish deposits and not leave a clear colour based indication so diagnosis based on colour is a lot more difficult. Mistakes can be done taking white or transparent deposit for a lean carb setting or manifold air leak.
However, heavy (black) carbon on the plugs is always from oil passing rings or valve guides. Beige/brownish carbon on the plugs is more normal. If that turns to (greyish) carbon or clean wet plugs, that can indicate excess fuel. Something wrong with the carburetor or a poor magneto that is missing ignition because of weak sparks. I'd say it again, with the modern petrol it can be difficult to read spark plugs.
4) If the oil level is OK in the crankcase then there is no reason to adjust anything on the oil pump. There is very little or no service job that can be done on the pump. The -31 pump has a few more details that might need an overhaul.
5) I would do a leak-by test with compressed air as suggested earlier, that would expose worn rings or other leaks right away. A compression test will compliment the leak-by for a good diagnose. A weak magneto can make decent sparks at higher revs, so the engine might feel "strong" through the gears but hard to start.