Same comment as the GP. I felt like you're breaking a convention by not having the logo go back to the chooser page, and by not returning to the chooser on refresh/revisit.
Website conventions?
We think of repl.it as a webapp, not a website. Once you load a language the app remembers your language and loads it for you on next page load, and if you want to change your language you click the language selector button (which I agree is not that clear at the moment).
Currently you can save a replayable session and get a unique link, but this is public. We do have plans to remember history locally (either just as command history or a full-blown session) in the future. The initial relevant issue is at https://github.com/replit/repl.it/issues/15.