I'm not at my C2 computer often during the week so I won't be able to look at it, but all the information you need to know is in the Real-Time Multiplayer example. Just look at the events and see how it sends input to the host.
If you see on the PEER object that it has a variable called "inputs" that is synced, and when the Not-Host pushes a button, it moves it locally AND sends that input to the host. That input is read by the host and makes your character move on his end. Since you're playing the same game it syncs up fine 90% of the time.
The left click action spawns lasers and such so that would be the best way to figure out how to make them see it, and you can use the same information to see how it processes being hit. Since it's basic it revolves around the PEER object so it won't give the most optimal way to handle secondary objects like the wall being destroyed, but it's all the same system so you can just make the wall sync or receive a message to be destroyed.
My first assumption I'd treat it like how player-damage is treated from the laser, but there might be a method that uses less bandwidth (unless sync only sends data when it changes, then it'd probably be pretty sweet)