Lisbon has a horrible housing crisis. Locals are barely (or not at all, in many cases) able to afford living there anymore, and airbnb has been there making the problem worse every step of the way. I hope the author gets plenty of evidence and reports this place to the authorities, then stops using airbnb.
Note that in Portugal garbage is usually collected from nearby (unsaturated green colored) lidded trash cans and dumpsters owned by the city government or entities contracted to it, where residents are expected to leave their trash. Lisbon does have a bit of a trash overload problem ongoing (more recent than the housing crisis), but there should always be a dumpster nearby where people can drop off trash for collection, leaving it right next to the container if the container is full. For this one single issue I imagine there was a miscommunication due to the language barrier.
Sometimes (speaking from personal experience), especially in a place so obviously neglected and unused, the toilet discharge issue can be as simple as grit or rust inside the tank preventing the part that drops to block off the water flow from moving, but it can be mechanically pushed down (or even washed to get rid of the grit permanently). Not to excuse the owner; just a possible way to make the author's stay a little less miserable.
It seems very hazardous to live in a place as damp as the author reported, damp enough that it attracted slugs and the water vapor likely got in the electrical system, causing a short circuit . Must be a real dump if it got this damp with the drought going on before this week. There are probably a lot of hazardous mold spores. They should have set up a dehumidifying solution immediately (three weeks ago); I would depart right away if possible.