I'd take JW's advice and look at in-gear vs. neutral for engine speed and vibration.
The hull is scummy, but not encrusted, so we know that the hull is not the whole problem. A few barnacles on the shaft, but nothing more than usual for this time of year.
If you've looked at the shaft, did you look at the prop? A few barnacles there can make a big difference.
He also told us to get a new fuel filter (and a "better" one than we have..racor R12P is the name on the filter).
Not sure what your friend meant by better--Racors are good quality. If they meant finer, unless your 2GMF doesn't have its own secondary filter, I think your 30-micron 12P is fine enough. But how old is the filter?
1. Bad alternator?
2. New filters etc would be helpful?
3. New engine mounts needed?
4. Anything else that we might be missing before I can a mechanic?
I'm not sure where you're getting the bad alternator or engine mounts questions from. You've got a mixed bag of questions/issues there. Maybe the RPM/power problem has made you look at your engine overall, which is not a bad thing. But to stick to what you stated as "the problem" if the engine revs freely when not in gear, I'd be thinking fouled prop and then fuel. If you don't know when the Racor was changed last, change it. But I'd stick with the 12P unless your engine doesn't have a secondary filter. If you do have a secondary and you don't know when it was last changed, change it, too.