When you rs+PW while carrying a friendly figure, does the friendly figure who had been carried get caught within the PW or does it stay off the map until the Action is resolved?

It gets placed back on the map after the movement, but before the Pulse Wave, so yes, it would get caught in it.

This is correct

There is one character, Takion, who can Hypersonic Speed and Pulse Wave so anyone he is carrying would be off the map at the time of the WHUMPF!