It depends if your transmission has a torque converter clutch or not, and whether it's functioning properly. Most automatic transmissions, at least electronically controlled modern ones, have a torque converter clutch. At higher speeds, or sometimes just in higher gears, the torque converter will be locked so it's spinning at a 1:1 ratio so you get better fuel economy. If it doesn't have one, then the RPM will decrease when you let off the throttle, though i don't think it should quite return all the way to idle even if you have no torque converter clutch, but it will decrease substantially when you let off the throttle.
Also, some automatic transmissions will go into neutral under heavy braking, but that's not really relevant.
It's not a bug. The physics calculations for a vehicle are paused during inactivity. Thus when there is activity again, it continues where it left off: the wheels spinning freely.
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If it's hydraulic then it doesn't have a cable. I personally doubt it's a problem with the hydraulics. I'd be more inclined to suspect the pressure plate or clutch disc. Though either of those would probably make quite a bit of noise if they were to break.
I'd be a bit concerned about the injection pump possibly not getting proper lubrication and getting also possibly clogged up when running cooking oil through it.
Does LFS simulate track temperature? Because if it's cloudy, the track will surely be cooler than if it were sunny. With my summer tires, I definitely noticed a difference from driving one morning that it was about 5C, compared to when it was sunny and 27C outside one afternoon a few days later and they were way more grippy. Dunlop Direzza Z1 (205/50r15), which for all intensive purposes are pretty much equivalent to "road supers" in LFS.
Though I noticed a difference between 27C and 5C, there isn't much of a difference between 27C and 30C ambient. Though, I haven't been able to test the performance of my tires terribly extensively. I plan on doing autocross this summer, so I shall get a better idea if I do so.
Fuel from the bowl is sucked into the motor from the air flowing past the needle valve in the carb. But something has to fill up the bowls. You claimed that there are vacuum powered fuel pumps. I have not seen any. I think you are mistaken. The bowl is either going to be gravity fed, as motorcycle carbs usually are, or there's going to be a pump filling the bowl.