While the tank is off for cleaning, be a good time to check the valve clearance, you'll be right there, easy job.
Clean the tank out with E85 gas. Slosh it around, dump it out, blow it out. Do not vacuum it out!
Depending on the condition of the tank, any aggressive cleaning can start it leaking. If it's flaking rust, might just want to buy a new tank and get over with.
If the tank is contaminated, the same will be in the carb bowl. You can take a fuel sample from the drain plug in the bottom of the carb. With the engine off, fuel valve open, get a clean glass, remove the plug, catch the flow. It should give a full stream, not slow to a drip or stop. Look at what was caught, if cloudy, there is water in the fuel. If dirty or rust chunks, the tank needs to be cleaned or replaced.
The carb may need to be cleaned. Don't be afraid of it, they are designed to be field serviceable and simple, They can usually be eased apart without buying a kit, cleaned and go back together. Plenty of online info and diagrams, just work over a clean surface so not to loose anything.
As for the performance...
Before disabling it, check the governor action. Looking at the carb, locate the throttle shaft. Engine off, dash lever at idle, the throttle shaft should be turned and held against the idle stop screw. then with the dash lever in the full fast position, the throttle shaft should be rotated and spring loaded to the wide open position.
Return the dash lever to idle, start the engine, watch the position of the throttle shaft as you suddenly bring the speed up. The throttle should immediately go to wide open, then modulate back as the engine speed comes up, and level off around 2200 RPM.
Yes, it is normal, necessary, to let the transmission coast down before attempting to go in any gear. There are no synchronizers, just a simple crash box.
Have you checked the oil in the gear cases? Those are notorious for having water in the case. It gets in from condensation and around the shifter boot if it's bad or missing.
If it's got water in it, drain it. Let it drip for a few days as emulsified oil will take a long time to drip out. You may want to flush it with diesel. Don't be tempted to remove the "plate" on the bottom. That is not a plate, it's the bottom of the hydraulic pump. It won't come out without further disassembly.
The transmission, intermediate, and differential cases are all interconnected. It holds 18 quarts. Originally it had 90w GL-1 mineral oil (not 90 w gear oil!). The mineral oil will work in warm weather, the lift will be slow in cold weather. A common substitute is 15w-40 engine oil, works better in cold weather.
BTW, the transmission grinding when going into gear can be aggravated by low oil level. The oil helps slow the spinning gears quicker.
There will be lots of questions, lots to learn, but it's all doable. A shop manual will be a valuable investment. Nothing better than having reliable information in hand when you need it. It will more than pay for itself in mistakes not made!