The watch does not "run down" any quicker with the chronograph on. It will stop sooner, but that is due to the additional loads that the chronograph adds. The spring runs down at the same rate regardless of the load.
You can leave the chronograph stopped in a particular position, and it won't damage anything. However the hand is now being held in place with the friction brake rather than with the hammer on the cams, so a large shock to the watch may move the hand.
Neither are a problem.
Cheers, Al
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