Need some help, 2003 Seadoo Rti LE RFI

[DookyDoo]

Bought a 2003 Seadoo rTI RFI LE a couple months back.it has a rebuilt SBT engine in it, 2 years old. Ran decent the first trip out. Second trip it started to overheat towards the end. And then wills start back up, but got it to eventually. Third trip my 12 noticed it was running rough, shaking, especially in idle. It died at the dock. I replaced the batter Roth there, but it just wills turn over. Did figure it was the battery at that point. Brough it home and put new spark plugs in it. Still would turn over. I have it a week of just sitting there, and seemed to be constantly draining excess of water out of the hull from time to time when I kept lifting it higher. This weekend, it finally cranked up, but seemed to be stuck in high rev mode, and a lot of water coming out of jet pump. I brought it out to the lake to just get it onto the water, and it was very sluggish, and still loud and rattling. I immediately turned back and loaded it back up. When I got home, I wanted to get the carbon seal. Although the guy I bought it from said it’s new. I noticed a cap with an o ring in it in the hull. I immediate though this may be my culprit. It took me a while to figure out what it came off off, but the rotax item number is one it. I found ONE online to purchase. It looks like it came from a place under the shaft/carbon seal. Down an to the left on the engine. I have been noticing a greasy grey metallic substance in the hull. It appears to be coming from that .the cap appears to be melted? I am attaching pictures of all this x I’m sure I have to replace the greas that has come out of the open area before I place the new cap on. I would imagine it’s running rough due to the loss of this grease. What is the cap used to cap off, and wheee and how much grease should I add back into driveshaft. I guess that is where this came from?? As you ca. see, I am a newbie to the jet ski world.