For developers.
Do you foresee in the free version with the next releases to remove the annoying advertising popups passing to the premium version?
In my opinion they are not effective in making users switch from the free to the Premium version, indeed it is a deterrent in the installation and use of the free version which is an excellent version compared to the competition. 
Premium version messages within the dashboard are fine but I would eliminate the annoying and sometimes misleading popups for novice users. 
You can get rid of ads by just unchecking the privacy settings or by turning on the silent mode.
While unchecking the privacy settings, pop-ups appear periodically. Or am I wrong?
Does the silent mode pop up pop-ups when malware is detected?
1. In my experience (using avast free) this doesn't completely remove them.
2. Silent Mode means just that, you won't receive an Avast Alert when malware is detected, you will be completely unaware of it.
Actions on malware detection would happen according to the Avast Settings. Ordinarily I have mine set to Ask (which won't happen with Silent Mode) as I prefer not to have Actions happening antonymously.