Actually you probably wouldn’t lose oil pressure with any of them. Worn seals and gaskets don’t affect the operation of the oil pump unless you run really low on oil. Theoretically you would maintain oil pressure with a messed up piston provided the engine could still turn over freely. Either it runs with those issues and you have oil pressure or the engine seizes. Oil pumps are driven off of the crankshaft.

Can you tell where the drip is coming from? Clean the oil off the exhaust and find the source of the drip is what I would do.

Can you tell what the fluid is? Is it just water, or could it be oil or gas?

Gas would be really bad and should be fixed immediately. Oil may be a small leak somewhere, and should be fixed but isn’t as urgent. Water is probably no big deal.

I suppose it might be possible if you way overfilled the oil. If you’re only a quart or so overfilled, that shouldn’t happen. Overfilling the oil could cause other problems too, though.

If you see oil in the exhaust, I would do a compression or leak down test to see if you can figure out if any of the seals around the combustion chamber have gone bad.

It may have a leak in the exhaust valve seals. You may be able to confirm this by doing a leak down test. If you hear a bunch of air rushing out of the exhaust during the test, you know the leak is coming from the exhaust valves.