Just a quick update. Here is the reply I received today - after almost one month - for my support ticket:

[My question was: I found out that Avast has a tracking module which uses Google Analytics code (at least) in the GUI.
Could you please tell me how to disable it?]

[i]<< Hello,

Thank you for contacting our support center with your concerns.
I cannot as I do not know anything about it or such avast! behaviour.

Best Regards,

Petr Bucek
Technical Support

AVAST Software a. s.
Budějovická 1518/13A
140 00 Prague, Czech Republic >>[/i]

Thanks, Mr Bucek! Now my faith in Avast Software is absolutely restored!!