What happened when you clicked the Update link in the first image you posted, that should have attempted an update ?
If it failed, what errors were displayed ?
What is your firewall ?
Does it allow avast.setup internet access ?
- If it does delete the entry for it and do a manual update, this should force the firewall to ask permission again.
Try this also if the above doesn't make a difference - From the avastUI, Settings, Updates, Proxy Settings, set it to Direct connection (no proxy), see image.