Heroku Workers are pro-rated to the second, just like Dyno's. So the second you shut it down, the timer stops ticking.
The time it takes to boot a worker mostly depends on your ruby application. The heavier it is, the longer it takes to boot up. Heroku spawns them fast, I think instantly because they are spawned from a compiled slug which is generated each time you push your app to Heroku.
The HireFire checkup interval takes at most 60 seconds, and less if more resources are available on HireFire's servers.