Weird.
Basically if I just uncheck SSL in Mail and leave everything else be, Mail will receive e-mails (and Avast will control them), but it won't sent them (it shows iCloud (offline) in outgoing Mail settings). After I switch Avast Mail shield off, all works again.
I will check if Mail will sent mails if I will leave SSL on (in other words not changing any setting at all and leaving Avast Mail Shield on - it should tell me it cannot control mails due to SSL connection, but Mail should still sent e-mails just fine) in around hour when I get home and will let you know.