[Phoenix-D]

"So one player sends out the information on turns and the others type their response and let the host play it for them?

Or do they get to actually PLAY the turn as if they were playing a hotseat game?"

They play it in Simultanous mode, send the turn file to the host, the host runs the turns and SE4 calculates the results.

Simulanious mode just means you input orders only, then at the end of the turn everyone's orders are run at the same time.