Lower than absolute zero?

Yes, negative absolute temperature is possible for systems that have an upper bound in energy. For example consider a two-level system for which in the ground state the lower level is fully occupied and the upper level empty. After 50% of the particles have been excited to the upper level, a further increase in the energy will start DECREASING ENTROPY of the system. But this means that the thermodynamic temperature is negative.

What Dr Zorro is saying will happen when T becomes already infinity, so going to the negative absolute temperature will require temperature hotter than the hottest. This looks paradoxical. But it is really not if we look upon the whole things as pure mathematics. It is very hard to imagine ∞ and -∞ at the same temperature T. But the real parameter is 1/kT = β which becomes +/- 0 corresponding to T= +/- ∞. Accepting some parameter becoming+/- 0 does not look paradoxical at all, rather it looks normal!

No.

First, absolute zero (despite some reports to the contrary) is the lowest possible temperature reachable in the universe.

Second, you can't "rewind time". Time only goes in one direction.

Let's just pretend that atomic motion describes all there is to know about temperature. The faster the motion, the higher the temperature.

So 0K is no motion. Reversing time, you have motion again, so will not be 0K any more.

If you could stop time, then you'd have 0K... but nothing less.

Absolute zero is when everything is practically frozen so you cant go below that.