Hello, Mike.
When I move my mouse to the upper-left corner of the screen, the left-bar of icons appears and all my windows zoom inward and arrange themselves ...
This is a Gnome Shell feature. You can use Gnome Shell under Ubuntu, of course, yet, the default desktop environment is Unity by now.
To the best of my knowledge none of the most common desktop environments in current Ubuntu editions, Unity, KDE, XFCE, offer this typical Gnome Shell feature.
To the best of my knowledge none of the most common desktop environments in Linux Mint 13/14, Cinnamon, Mate, XFCE, KDE, offer this typical Gnome Shell feature.
When I alt-tab, I see one icon for each copy of a program. I see icons and not thumbnails of the windows themselves
The current Cinnamon 1.6.7 desktop environment, available in Linux Mint 13 & 14, allows you to alt-tab through the window list as well, and will display thumbnails of all windows plus a larger preview of one of the thumbnailed windows as you alt-tab through the list.
When I reach the login screen, my username is displayed read-only ...
The list of available login-screens depends on the desktop manager. Mint 12 uses LightDM. Mint 13/14 use MDM by default. The current MDM offers a long list of differently styled login screens, some of which seem to behave as you describe. In Mint 13, you can configure MDM and the login screens by going to Menu => Preferences => Login Screen.
So I guess that the features explained under bullet points 1 and 3 can be achieved under Mint 13 / Mint 14 as well, by selecting the appropriate desktop environment (Gnome Shell) and by selecting the appropriate login screen. But be aware that by selecting Gnome Shell just to activate one particular feature you give up a lot of the typical design and interface features which make Mint look and behave like Mint.
Personally, I happily lost the feature you love so much in favour of Cinnamon. - By the way, you can achieve a similar behaviour in Cinnamon by moveing the mouse pointer to the utmost upper lefthand corner of the screen.
The best approach, though maybe not the fastest, will be downloading 2 or 3 Mint live systems (Mate, Cinnamon, KDE), run them from DVD or USB pendrive and find out how they feel and which one you like best.
Kind regards,
Karl