So the WS is checking ONLY web-browsers and e-mail actions?
Most likely yes since Web Shield monitors HTTP traffics while Mail Shield monitors SMTP (sending messages), POP, IMAP (Both for receiving messages) and NNTP ports (Receiving News). The "formula" for the ports where AvastSvc.exe staying is 12000+the monitored ports. As I have already mentioned, for instance, 12080 for HTTP, or port 80.
So the WS is checking ONLY web-browsers and e-mail actions?
Web Shield is only checking HTTP traffics for remote port 80. Email traffics are checked by Mail Shield although the process name is the same AvastSvc.exe.
Other programs does not able to use the WS "proxy"?
As long as
Web Shield is concerned, it only checks HTTP traffics initiated by the supported browsers to remote port 80 by default. If you are talking about AvastSvc.exe, I said most likely since I don't know how P2P/IM Shield works since I don't use any P2P or messaging applications.
If i allow AvastSvc.exe to connect on HTTP and e-mail ports is this means what Avast! is know all about my browsing/e-mail activities?
About Web Shield, yes as long as you use the supported browsers I aforementioned to connect remote port 80. As for Mail Shield, the story is bit different since it seems to monitor any traffic which goes through ports such as 25, 587, 110, 143, 119 not concerning which application is using them.
Why AvastSvc.exe sends ICMP packets to home (Avast!) servers?
It's checking for possible update.