We do have an inbox that sorts messages onto a separate page from replies to posts. I think the easiest change would be to simply make two separate icons for these two separate pages.
I don't think this is correct. I'm only familiar with http://lesswrong.com/message/inbox/ , which mixes the two together. You may be thinking of http://lesswrong.com/message/sent/ , which shows all the private messages you've sent.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.