The SpaceTime algorithm allows you to run the Reverb either in series or in parallel with the two Delays (which are actually in parallel with each other).
The VERB LVL knob is divided into two distinct sections through its travel. In the first half, the Reverb is in series with the Delays and in the second half, the Reverb is in parallel. If using H9 Control, press the "Pedal View" button in the top left corner of SpaceTime's parameters page to view the routings.
Regarding ping pong delays, the Delays in SpaceTime are in parallel as stated, but the feedback paths are not setup for a ping pong effect. You would need an external device such as a mixer with sends and returns to get a ping pong effect by setting up the proper feedback network. Additionally, with the Reverb routed in series with the Delays you would get Reverb sent back through the Delays as well.