I noticed that the crystals near the bottom of the pad and close to the logo area do not heat up. Is it supposed to be that way?

It is OK if not all stones have equal heat. 

The first and last tubes are not directly heated by the heating system, which goes through the whole mattress in a “snake” configuration but cannot come close to the edges of the mat due to safety reasons.

When the mat is hot for a longer time, the end tubes with crystals will absorb heat from the other nearby stones.

It doesn’t affect any function of the mat. Your body is receiving the deep heat, negative ions, and far-infrared therapy it needs.