<p style=”text-align: left;”>You have 2 problems, then:</p>
1. The blocked breather – should be easily addressed.
2. The pump coming on all the time. Save for the remote possibility of a duff pressure sensor in the pump this can only happen if there is an air or water leak somewhere. Given that you have fresh water in the bilge you certainly have a FW leak. From what you said about the state of the tank you may have an air leak as well as a water leak. Both can be a struggle to deal with but at least there is near certainty that you are looking for leaks, not pump issues.
It is worth checking your transom shower. I keep meaning to permanently disconnect mine (little need for it in Fleetwood); check the tap is off and that there is nothing coming out of the shower head.