In word 2013 - what is the shortcuts for removing the left side panels (eg-search) & right side panels (eg-research)?

Both Navigation and Search panes have X buttons to close them. AFAIK, there are no keyboard shortcuts for closing them. You can, however, assign a keyboard shortcut for the Navigation pane, which responds to commands for its former incarnation, the Document Map.

1. Right-click on the QAT and choose Customize the Ribbon.
2. In the Customize the Ribbon dialog, click the Customize button next to "Keyboard shortcuts."
3. In the Customize Keyboard dialog, in the Categories list, choose "All Commands."
4. In the Commands list, scroll down to ViewDocumentMap.
5. In the "Press new shortcut key" box, press the key combination you would like to use to open/close the Navigation pane.
6. Click Assign, then Close, then OK to click the Customize the Ribbon dialog.

You can follow the same procedure to assign a shortcut to the Research command, which, despite the description, is also a toggle.

The left hand find panel is also the old "Document map" or new "Navigation Pain" <sic grin>.  You can toggle it using <alt><v><d>.  That is the good old MENU alt shortcut for View menu > Document Map. It was "grandfathered" in for those of us who were used to the menus. It still works in 2016.

You can turn on the Research pane using the <alt><S><RS>  . Unfortunately MS did not see fit to allow it to turn off the pain.

You should be able to at least turn on most of the right side panels using <alt> shortcuts. Press and release the <alt> key, the alt shortcuts for the tabs will display. Press and release the appropriate tab shortcut to display the button shortcuts.