Plastic thru-hulls are not allowed per abyc standards for below the water line use. An older boat will have them, and they may be grandfatherd in. They will break easily as they age and sink you in a hurry.
As suggested, more like a fuel/carb issue. But I've also seen the weights in the dizzy under the trigger plate go south, timing will be affected. Just another tidbit to check out when all else fails.
I second the tiller arm. Most tech's don't know it, but it should be checked when the drive is serviced. There is a torque spec for the pinch bolts. If they are loose, it will eat away at the square arm and ruin it.
Is this a new to you boat? And if so, how long did it sit before you got it? And how about a model/serial number of the motor? If you just aquired the boat, we can diagnose with a few questions.
i would not. There would be debris possibly in the water, that would damage the pump, alge would soup up the system, and smell bad. Cleaning tablets may work but reguardless, I wouldn't do it.
Because the bushings get lubed by the water. My brother in law would dip his fishing reel in the drink if it squeaked. It worked till he got home and cleaned/lubed it up later.
Slow shifting results in the shift dog inside of the lower unit rounding off the teeth. That grinding you ear is that happening. Shift quick, but not so far as throttling up. Lower shift cables need replacement once in awhile. I'm 7 years into my last replacement, maby I'm lucky? dunno.
Something about that don't look right. Usually there is a backflow preventer on the fitting. Did it come out with the hose? Edit, Looking closer, it did. The hoses are on the part that came out.