Is there some simple way to have a pop-up reminder accompanied by an audio sound (like a bell) show up on my screen at 40 minute intervals? ... I don't know if this would be an application, or if there is something in the OS (like Task Scheduler) that would do the job.
Yes, you can do that sort of thing in Task Scheduler quite easily, although the UI on Task Scheduler will take some learning. Also, most email programs include calendar/reminder features, but those are meant usually for daily/weekly kinds of calendaring. Task Scheduler should theoretically work for what you want. It has an option for the task to be "display a message".
Note sure about the 40-changing-to-30 thing, but for a start you could just do 40 and that should help immensely.