1) The boat runs fine. Am I tempting fate to take it out?
2) Are there options other than replace it? Clean out the screen? Fuel treatment? Other?
Would changing that filter help?
If the boats fuel pressure is reduced, your motor may run lean. A lean running motor will destroy it self over time.
If the pump is OK but having trouble getting fuel due to a restriction in the line, a fitting or fuel filter, given enough time the pump will be damaged.
Yes, changing the filter would help if it's clogged or the seal is leaking. If the filter has not been changed this season then do replace it. The plastic cover is removed to gain access to it
3) How difficult is it to replace myself? I suppose I remove the alternator to access the filter - then...
4) What is the purpose of the CoolFuel item in the photo below.
The hardest part in replacing the fuel pump is getting at it. The cool fuel module is on the port side down low and behind the motor mount. The plastic cover comes off easy with a couple plastic clips. Once off you can see the fuel pump and the cooler tube. As Pete104 mentioned your pic is the fuel filter
5) Is there anything else I need to do of a diagnostic nature?
You will need a high pressure gauge and a fitting to check the fuel pump output.
Don't know if a booster pump was added but your motor did not come with one. If one was installed it will be next to the fuel filter.