Hey there, CubPilot!
From what I could see, it seems to me you are trying to steer the aircraft while its tailwheel is unlocked. The PT-19 has this tailwheel locking mechanism, which may seem odd at first, but a breeze once you get the hang of it. Too much rudder input will cause the tailwheel to "snap" out of its locked position and will free castor. This is useful for tight turns on the ground, but it makes everything else pretty much impossible. To lock the tailwheel back in its place, you must first bring it under its "lockable amplitude" (which means it must not be too far left or too far right from the center of the rudder), and then push the stick back in order for the locking mechanism to work. You'll hear an audible, metallic "clank" when locking occurs. After this, taxiing the aircraft should be done with moderate rudder input if you don't wish to unlock it again. Using differential braking makes this a lot easier, even though it seems very hard at first!
If you don't want to deal with this, you can simply go to the 3D menu and select to have the tailwheel always locked. This will make the PT-19 behave just like any other addon you're familiar with, and the tailwheel will never be unlocked again. This is a convenience feature.
About imbalances: If the aircraft is fully repaired and functional, one thing that often takes pilots by surprise is the fact that fuel tank management must be done manually. The aircraft has 4 fuel tank selector positions: 2 Both OFF, Left and Right. After about 15 minutes of flight or whenever applicable, you should manually change the fuel tank switch position to the other tank, as it may become out of balance otherwise. Other than that, the PT-19's flight model does take into account the natural yaw tendency of the real aircraft. This means that, even if perfectly balanced and trimmed (elevator trimmed), you must always give it a little rudder input here and there in order to have a smooth flight. Flying this antique aircraft requires way more hand-feet coordination than modern GA aircraft, but it is a worthwhile endeavour!
And finally about grass vs pavement performance... This is a known issue with how X-Plane sees grass and pavement. Unfortunately, the PT-19 does require more RPM than it should in order to start moving on grass, and extensive testing show that it does require about 150-200 more RPM than it should in order to break inertia and start rolling. The PT-19 in real life does behave like this on grass, but not to THAT extent. Unfortunately, this is a limitation on the simulator's end and how it "sees" the ground friction values, and changing this behaviour would break the accuracy of the aircraft's landing performance.
I hope this helps you somehow! Please feel free to follow up with questions or comments!
Respectfully,
Dan.