Possibly your clutch needs adjusting, also.
It sounds like the main issue here is you're used to driving an automatic transmission vehicle, where once you place the shift in Drive (or R) the shift stays there, and you use the brake to stop and the accelerator pedal to go. With a tractor you're (usually) to depress the clutch, choose a gear you want to be in, set the throttle lever to appropriate engine RPMs, then let the clutch pedal out to engage the drive to the wheels. Let's say you choose 3rd gear, 1500 RPM throttle, let the clutch out. When you want to slow down but stay in gear, let's say if you're on the road, you reduce the RPMs.
If you're working the machine and need to stop temporarily, let's say to pause brush-hogging to open a gate, you'd reduce the engine speed to low idle, push down the clutch, shut down the PTO, then put the shift lever in neutral, let out the clutch, set the park brake, and go open the gate, staying away from the rear of the tractor. Once through the gate, push down the clutch, engage the PTO, shift to the gear you want, increase the engine speed to the sweet spot, then let the clutch out and mow.
When you want to change gears, you push in the clutch, then step on (both) brakes, wait until you stop rolling, change to the gear you want, then let the clutch out again. Most gear tractors are shifted only when stopped, with clutch down. Normally you want the engine to operate in its comfortable power range, so you don't change the RPMs. In a shift car, you're moving much faster than a tractor, so it's harder to coordinate gas pedal and clutch. In a tractor, the clutch pedal is more like an on-off switch: you let it out relatively quickly, like over the count of one-mississippi (or one-louisiana).
You must push in the clutch pedal to slow or stop every time, as you need to disengage the engine from the tires.
So many have tried different ways to explain this to you: too many words! This is hard stuff to get in writing, but pretty easy to have someone show you. I think it would be as many have suggested your best plan to get someone to show you how to run your machine. Should take only a half hour or so, then you'll get the hang of it. You need to get this info for safety, and to be sure you're not wearing out the clutch or brakes by having learned bad habits.
Best luck, Jim