Go to the analytics top folder. The list of possible reports appear on the right. Select one, customize it and then click "report actions" -> save as.
Pay attention that you can save to your personal folders (for your eyes only) or in group folders (Shared with every one).
Yes, that is the new functionality.
Select report from your right hand side of the screen form your Analytics tab--> Selct report you wish to create--> When you are done with editing your setup or smart list of your report--> Click on the Report name tab --> Report Action drop down select Save as.
Here is a document to save reports