In other words, if motor is supplied with stall current for more than few seconds, it will get damaged by heat. So, one just needs to monitor the current going into the motor and it gets as high as 90% of stall, immediately disengage.
Yes, that would do, except the 90% would need some calibration.
The datasheet might be a bit conservative and overstate the stall current, so you might miss the failure point until it releases smoke 
How can one use Hall effect sensor to measure movement. You thnik attach the magnet to the shaft and than measure Hall effect current/voltage?
Yes, that's the idea. The Hall sensor will give a nice sine wave as the magnet spins past it. If you're only spinning at, say, 20,000rpm or less, then you could read it with an analogue input. If you want much faster, get a Hall switch IC, and read the digital input.
What percentage of the stall current is optimum for continuous running of the motor?
I believe it depends on the motor.
Very well specified motors, with good datasheets, will give the torque vs current curve. When you look at it, you'll see a 'knee' where it quickly reaches stall.
[edit]There are some examples about 60% of the way down: LEGO 9V Technic Motors compared characteristics
Some motors are specified directly for efficiency like this: MFACOMODRILLS.COM
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AFAIK, its good to keep well away from that knee, so that reasonable variations in opposing force doesn't trigger the thing stall. It can be run closer to the knee if the variation in force is small, or there is a good way to protect it (i.e. good stall monitoring which will quickly switch it off).
Sorry to be vague, but "More Input" 