Shouldn't the "verbose" option take care of the presence of the status or progress messages? Also, arguably, the error and warning messages are status messages too, so I would say all the status messages, regardless of gravity, belong to the same channel.
Error and warning messages are not status or progress messages, at least not in the context of this discussions, which is that a long-running computation should indicate to the user that it's doing something.
Example: "warning, the x is in y condition and thus z will take place affecting the computation in progress" or "error, could not perform x (out of many x-like things to do, but I'll continue because you instructed me to)". These are status messages in a long-running computation context.
I disagree. They're a warning and an error message, and should go to stderr.
It may _also_ be useful to show them on the terminal, in case the user would like to see them now, and has redirected stderr somewhere other than the terminal. In that case a program might show them on /dev/tty as well.
