negative kinetic energy when tunneling?

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As we learned, quantum particles can tunnel through a higher energy barrier.

1. But the price would be having mathematical negative kinetic energy or imaginary velocity. How to understand this?

2. In the higher potential region, what can the partical do (stuck and stopped, or localized to a smaller region bouncing back and forth)? Still forming partical in a box pattern or just exponentially die out?

3. If the particle penetrates a barrier without any friction and enters a box, will it's energy/wavefunc change/recovery and how?

Thanks in advance.