Our shower has a dedicated sump and a dedicated pump separate from the bilge pump, the drain for the icebox also drained into it. This than drains directly overboard.
As far as the ventilation goes, I would think that the propane water heater would draw oxygen in the same way that my bulkhead mounted propane cabin heater does.
The flute or chimmney has two chambers, a sleeve with in a sleeve. One draws air in from outside of the cabin and one exhausts out. This set up should never become a problem.