Lion/Mountain Lion Mission Control used with CTRL+# (10.6 Spaces-like)
In Lion, by default, will switch to a particular Desktop if you hit Control+Desktop's Number. Go to System Preferences / Keyboard / Shortcuts / Mission Control and check if you've overwritten this shortcut. 

Yes, you can configure a particular App to open in a particular Desktop. To do so just:


Navigate to that particular Desktop.
Open the App you want to assign, if its already not on the Dock, and right click on it.
A contextual menú will show up. Under Options you'll see a submenu called Assign to and three different options. All Desktops, This Desktop or None. Select This Desktop.