I've sent a few mails to the Ayatana mailing list regarding some UI suggestions for Unity, but I'm afraid I keep confusing the right terms for the UI element, so I would like to have some clarification.
Is the bar at the top called "panel"?
Yes, the top bar is called the "unity-panel" or simply panel, the container for indicators and global menus.
Does the Ubuntu logo at the top left corner have a name?
Is the left sidebar called "dock"?
It's called the Launcher.
Are the coloured tiles with app icons on them called "launchers"?
Launcher icons or Launcher items.
Is the purple tile called "workspace switcher"?
As of 11.04, yes.
Are the fullscreen things that appear when you click the Ubuntu logo, the Places tile or the Apps tile, called "dash"? Do they all have the same name?
Right; Dash is the component name for the overlay that's used for Applications and Places. In non-technical contexts it seems to be used as the Applications Dash and the Places Dash.
The first thing you'll see when opening the Dash is the Dash Home. Without typing or clicking anything, the Dash Home will show you applications and files you've used recently.
There seems to be no term decided upon for items kept on the launcher via the "Keep in launcher" function. The relevant dbusmenu functionality is named "pinning_item" in the code; "sticky" doesn't appear anywhere in the wiki and bug reports, and "Favorites" is used in the architecture document once and somewhat ambiguously to refer to what seems to be the "pinned" application items. So "Pinned" and "Favorites" seem both fine for now.
Status Menus (Indicators)
This region also contains the Notification Area, disabled by default.