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.
No, the top bar is called the "menu bar".
It's called the "home button" though it's jokingly referred to as the BFB by developers, for "Big Freaking Button"
It's called the Launcher.
"Launcher icons" or "Launcher items".
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
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.
Ubuntu from 11.10 up