Welcome to the forums and the avast family.
As you have found there is a vast amount information on the forums, many don't find the search function though
You can do as You have with providers that you don't use, they would only be required if you used the associated applications. You could go a step further if you wish and actually uninstall them (windows add remove programs, avast! Antivirus, Change/Remove, Change, scroll down to the providers you wish to uninstall and uncheck the option).
Since you disabled them (? Terminated) they aren't actually running they won't be using any resources only taking up a little HDD space, you could just Terminate them and answer Yes to the question to persist the changes.
If you are using a download manager, etc. where you can give a location to scan them, then you could have avast scan them. Assuming that you installed avast! in the default folder, this is the path needed to scan downloads, C:\Program Files\Alwil Software\Avast4\ashQuick.exe
If not then there is no problem in scanning them manually as it is a good practice as by default zip, archive files aren't scanned as they are inert.
I would say the problem may lie with ZA, though it might be worth running HiJackThis to see if there are any remnants. Program & Tutorial - Also useful as a diagnostic tool -
FileHippo Download - HiJackThis - HJT Information
HiJackThis Tutorial.
You could post the contents of your log file here.
