The Mackeeper thing probably never allowed a correct installation of Avast!! You keep blaming avast for the stuff that mackeeper did to your mac.
What you put on the login is launching the avast application, when it says avast is not running it's referring to avast background services which should be started automatically
Uninstall avast by opening avast, going to the avast menu on the menu bar at the top and choose uninstall, reboot, install avast again.
I'm out of this this thread, good luck!