Pistons can be done with the motor still in the machine.
As for the kind of machine. Yes it is a Bombardier sea-doo, but what model is it? It would help us give you more information if you could tell us WHAT sea-doo it is? There are many different models, motors, carb configurations.
Based on what I'm seeing with those plugs tells me you could have one carb giving you trouble, if it is a twin carb model. But based on what you are saying it sounds like you have had a seizure of one side, possible not severe, and it is still functioning to some extent. This is a scenario I have seen play out before, I have a sled right now that runs great all day until you give a good wide open shot and it binds up one piston but will not die.
There are many possibilities as to what is going on with your machine and just rebuilding it without finding the root of the problem is not going to help in the long run.
Take pictures of the machine, motor and carb area so we can help out.