For instance, if I want to be reminded every N numbers of days starting with a particular date, is there an app or category of tools that can accomplish the task?
While not a specific software recommendation, your requirements are met by tons of apps called "calendars" having a feature called "reoccuring events". They'd not only let you define a start date and interval, but an end date as well. Example: "Starting on May 26th, 2017 and until July 28th, 2017, weekly at 11:00pm, remind me to have a break from TV" :)
Sometimes the most obvious and easily available solutions slip through the nets of our brains :)