It could also be a problem with the controller, or position feedback system. A properly tuned system should compensate for normal variations in operating conditions. Maybe some adjustments to the PID loop is in order.
It is possible.....kinda It would require a step & direction to analog converter, they do exist, but tuning might be a nightmare.
Seems reasonable to me. It would be possible to hang a servo motor onto a rather inexpensive gear pump. What size motor is it going to take to drive the pump?
Your operating sequence sounds reasonable. To prevent the leak if needed could be done with pilot operated check valves.
Yes, you would just feed back all of the operating conditions to the computer and let the computer figure out how to follow the motion profile. This may require a controller a bit more sophisticated than Mach3. The Kflop/Kanalog is user programmable so might be an option. I think you are going to need some special software. But it sounds like you are already a programmer, you just need to dive in a bit deeper. Should be a short learning curve, and a really fun project.
Absolutely, that's why PID loops were invented.