Cannot access any websites { other than google, yahoo, gmail, youtube and facebook (http type) } on macbook air
Assuming the actual issue lies in the fact that Avast has messed with some of your connectivity settings, I recommend re-installing the software, followed by performing another uninstallation.


  (((Avast has some pretty good instructions letting us know that throwing it into the trash does not uninstall the software for Avast (I know your explanation mentioned you clicked on uninstall, but I'm just  covering basics here).)))


Avast Official Instructions:


Click the Avast Menu bar icon  on the top-right of the screen and
select Open Avast to open the Avast user interface,
...alternatively, open Finder, go to Applications, and double-click
the Avast icon.
Then click Avast in the Menu bar on the top-left of the screen,
select Uninstall Avast,
...and when asked to confirm the uninstallation, click Uninstall.


Source (has pictures to follow).