That cable on the left is your reverse cable. It's going to need to be replaced. The plastic nut that holds it in place should be replaced with an aluminum one as the plastic ones are known for leaking.
That impeller is pretty tore up. You should send it off to have it reconditioned or replace it altogether. The leading edges should be smooth, not jagged. While you're at it, you should replace the plastic wear ring as well.
How does it sound when you spin the impeller? If it's rough or sounds kinda loud, you may need to rebuild your pump as well. On the back side there's a cone with three allen head bolts holding it in place. When you finally get the venturi off, you should remove the cone to inspect the grease in there. There should be no water present behind that cone. There should not be any rust on the rear bearing either. Once you get it off, post pics.
Driveshaft splines look good. That impeller may cause some cavitation due to it's condition, but not something that would limit your RPMs, just give you a poor holeshot and reduce your top speed.
Let us know how the battery load test goes as well as the leak down test. That boat appears to have been run in salt and not properly taken care of. Everything is fixable so far, but I'd hold off on replacing anything until you get the leak down test done. No point in spending money on things yet if you have motor issues.
Welcome to boating. It's not a cheap hobby, especially when you're fixing other people's mistakes, but hopefully you can get the boat up and running soon.
