FYI to anyone concerned.  The two features mentioned in the title of this post are exhibiting different behavior in 12c vs 11g.

Recent Items - In 11g, the list of the 9 most recent items that you have touched persisted between sessions under the 'Others' heading.  Now the list is no longer visible after signing out and signing in.  It starts over with every session. 

Start on Criteria Tab when Editing an Analysis - Setting this option in My Account does not "stick".  It immediately changes back to 'Start on Results tab'.

The above statements are applicable as of March 2, 2016 and version 12.2.1.0.0 on Windows, with no patch sets available yet.