I'd never leave a motor activated, even if not rotating, while making measurements. Off should be off, or clutch disengaged, otherwise one is courting disaster. Neither would I use the emegency stop, except in an emergency. Depending upon the setup the ES may well stress the components far more than an orderly stop using the normal button
The large currents when starting an induction motor direct-on-line aren't really to do with inductance. When running at rated speed there is a significant backemf induced in the windings from the magnetic field associated with the rotor. The current in the windings is dictated by the small difference between the applied voltage and the backemf. When starting the backemf is not present, so the full voltage across the windings means the current is correspondingly large, until the motor starts rotating and the backemf appears. With a VFD the VFD simply ramps the voltage up slowly to keep the current at a sensible level.
In theory an induction motor can be run at 0Hz. The systems I worked on for electric vehicles did just that, full torque at zero speed. It's the equivalent of holding a vehicle on a slope by slipping the clutch. Whether the facility is needed on a machine tool is another matter. One also needs to consider the VFD. A simple V/F unit won't be able to control at 0Hz, you need vector control. Originally you also needed an independent measure of rotor position, but there are now sensorless vector control units.
Again in theory, an induction motor can be run above it's base speed, usually at 50Hz in the UK. What happens will depend upon the motor design. If you supply a nominal 50Hz motor with 100Hz it will try to run at double the speed. Whether it does so, or flies apart will depend upon the mechanical design of the motor.
To summarise there is no problem, in theory, running an induction motor from 0Hz to 1000Hz, but as always the devil is in the detail. I think most general VFDs only go up to 400Hz, which is nominally 24000rpm for a 2-pole motor. That's what my high speed spindle on the CNC mill goes up to.
Andrew