Dave: I can add to this post tonight, but here are few suggestions to get you started. Others will have more suggestions,
Bookmark this following link for its diagrams:
Buy OEM Parts for Yamaha, Waverunner, 2007, SUPERJET - SJ700BF
www.partzilla.com
We try to purchase parts from
@JetManiac and
@john zigler but sometimes have to resort to partzilla.com
Takes some more photos of the engine compartment in your ski and in addition posting them up here, just look at them until you can identify each item.
Don't work on it, just look at it.
The engine on your ski has a number of systems. Try to identify which goes with which:
Air Intake;
Fuel;
Exhaust;
Spark creation, timing and distribution;
Battery and electric charging
I looked for you for an actual oem Yamaha SERVICE Manual on ebay, and couldn't find one for your year. But look and save your search. Make sure it covers your model year.
Try to resist the urge to work on the engine of your ski without knowing what it is you want to do and have thoroughly determine the best approach to do it.
There will be times when it is broken and you have to take thing apart to test them, but resist the urge to take things apart now without a reason.