We just got a 2007 35ZR, it was a repo so we didn't get the manuals with it, in front of the starboard motor there are two handles attached to cables and they go to two ball valves below the motors that come out on the top of the notch at the transom. What are they for and how should they be when running, valves open or closed? By the way it has 525EFIs

The handles obviously open and close the valves. The valves are put in to release the vaccum that is caused by the notched transom. You should always run with them open.

First congrats on your new boat.. The 35ZR is an awesome boat. 496s she runs low 80s and 525s runs 92.. I have ran several Poker Runs with a 35 and she handles like she was on rails. Yes: The valves are for vent blow off and helps get the air thats trapped under the transom out, so the boat gets on plane faster and keeps any prop blow out down to a minimum. The valves are there so they can be shut down if a leak ever occured... Smart thinking on Donzi's part.
Best of luck with her you are going to love the boat.

What props were being run to get low 80s with ho engines?

Bravo 1 151/4 X30 pitch running saltwater.