Hi Trent,
Let's knock off one thing at a time. Item 3 is the one which happens in desktop browsers (for you), so let's deal with that one first.
I'm on windows 7 here, and I've got all the browsers - but Firefox is the easiest to debug in, so let's concentrate on that.
What I did was this,
Run Exe.
In Firefox go to
http://127.0.0.1:88/click login button
login screen opens - demo / demo populated. I click Remember Me to yes.
Then Login button.
the page refreshes, login and password are still there, Site field has appeared. It's a drop-down with Sydney and Melbourne. I select Melbourne.
In Firebug Console (firefox extension) I see a request is made to the server, and a reply comes back. The reply includes the <select > box, and also the 3 options, the Melbourne one is marked as "selected".
I then click Login again and I'm logged in.
Perhaps try it on your side, in a new clean folder, and see if you get the same, or if you diverge from the path I've explained above. Clearly there is a difference in what you are doing and seeing to what I am, and identifying that difference is very important to understanding why you are having problems.
As an aside, I performed the same path on the phone, and got the same results - so I don't think this item is a desktop / mobile thing.
As another aside, I'm going to discuss this example in the webinar today (_if_ I remember <g>). I know it's a horrible time of day for you, but maybe grab the recording. I think perhaps the work-flow of this screen could be improved a lot and I'd like to show how that works. Needing to press the login button twice is a very ugly approach from a UI point of view, and I want to demonstrate how you might tweak it to work better.
cheers
Bruce