Why the amplitude jumps between 0 and 5v, and the frequency jumps between the value in the set (or a multiplied value based on Frequency Limits) and zero?

That's because there is a gate in the setting. You're experiencing a safety feature to protect Spooky Central. Please check here to change:
http://www.spooky2support.com/hc/en-us/articles/219297797

"The software changes from green to pink screen and the voltage on-screen shows 0. However, the plasma tube is still lit and the Spooky2 frequency generator is still transmitting a signal. I had to shut off the Spooky2 Central unit to get the tube to turn off."

It means your generator has lost communication with Spooky2 before you turned off the software.

High power and high-frequency signals are emitted from Spooky2 Central. These are affecting your generator. The USB filter cable and high-quality Spooky2 Central BNC cables prevent most of the frequencies from entering the generator. However, the generator's body is made from metal, and this is picking up frequencies from the white high voltage cable and the tube. Please have the white high voltage wires and plasma tube as far from your generator as possible.

You can learn more detailed from the link:
http://www.spooky2support.com/hc/en-us/articles/216038418