How do the dark spots look in the new growth?
If they turn orange first, then brown, then black, it might just be something with calcium availability (pH of the soil being too high or too low, pretty common in older plants that are commonly kept indoors).
Keep in mind that cutting off foliage that might be infected does two things: it can contaminate your tools and spread to the other plants (use 70% ethanol/alcohol as disinfectant, soak for 15 minutes, adding a little soap or shampoo really helps).
The second thing: Plants respond to infections way differently than we do, so if we remove an infected part entirely, it might not want to fight infections on the other unaffected parts - if you remove one bad tooth from your mouth, it's easier to forget to brush your teeth because they don't hurt as much compared to when the tooth is still there and keeping you awake at night. While plants do have an immune system memory of some sorts, it's sometimes to better to leave damaged parts a little longer.
Cutting stuff off also stops you from seeing if the damage progresses on old foliage, it only gives you a view of the newer parts. Especially nutrient issues can easily be overlooked if we only keep the newest parts
There's a fine balance between cutting something off being the best option, and keeping something on as the best option. I've made the wrong choice on many occasions.
Anti-pest stuff is usually aimed at bugs, insects, mites and such. If you want to fight bacteria, use bactericides. If you want to fight fungi, use fungicides. A bug spray doesn't kill fungi.
Something for us all to remember: no plant dies within a week unless it's cooked or dried out. It's a process that takes months, sometimes years. We humans can take our time for proper diagnosis before we act. And if we can't, then we were already at least a month too late.