Turning off all or some Avast sounds can be accomplished either through the Avast program settings in the menu (right click tray icon, program settings, sounds) or via the speaker icon in the system tray, or via sounds in the control panel.
BOAC, I'm not too versed in the way of firewall protocols; I don't know what a UDP flood log represents. (Doesn't sound all that great, though, does it?)
With a hardware firewall guarding the gates it would seem highly unlikely to me that anything nasty would have arrived down the web, unless you actually invited it, so I think you can probably relax.
An excellent "second opinion" antispyware scanner is
MBAM (free and paid versions available.) This is the current "rock star" of the rogue scene, and it wouldn't hurt to scan with it, if only for added peace of mind.