What kind of times can I expect to see between changing my code and having it run on the Internet? And does this go away?
It shouldn't be more than a couple of seconds between you making the change and it being updated in your live app. And projects remain up permanently if you log in (projects by anonymous users are removed after 5 days).
How long is “permanently” supposed to be?
As long as HyperDev keeps going, but it doesn't lock you in - You can get a zip of your code, or export it to directly to GitHub, and it’ll work without any changes on other services.