What the heck happened to your carrier seal. The grease is supposed to go inside of it not on the outside. Water could be coming through the carrier seal if the seals are bad. There are two seals on it. One towards the outside to keep water out of the bearings, and the second at the end you can see to keep the grease inside. Best way to check is lower the ski on the ramp and start it up on the trailer in the water and observe if you can see water coming in. Or ride it with the seat off.
Also you might have a water leak coming from the cooling system. Bad gasket or maybe leaky exhaust pipe or bad/loose cooling hose. All these things can be checked running the ski on the trailer in the water. You want to do this in the water so you don't burn up the carrier seal which needs water to keep it cool while running.
Yes the rivet holding the traction mat on goes right through the hull. So water will get in through that hole. Is it enough to fill the ski? I would say not when it's running as the bailers would pump the water out. But it will definitely be a source of water getting in when stationary.
And lastly, unrelated to your water leak, I am not sure what happened to your pto rubber boot but it looks like the end was cut off. It is supposed to be full of grease and the small end is supposed to have a clamp on it to keep the grease inside. There is no room for the clamp anymore.