auggie doggie, have you compared your m.southwest.com suggestions to southwest.com functionality? Reading through your list I get the impression that most of your requests are for changed southwest.com functionality (#1 being one exception...except that you still have to log in even with southwest.com; the "remember me" feature only pre-fills the RR# field for you; I have no idea whether mobile devices have form auto-complete functionality, but the "remember me" checkbox does nothing that you don't already get with form auto-complete in your computer's browser).
Regarding your #3: there
is a logo (

) that
looks like a link to the home page...but it isn't. You are correct that it should be a link, but I wonder what the browser back/history feature is like on a mobile device; maybe you can just use the browser history list to go back to the home page?