Unfortunately as an avast user like yourself, I cant say why (other than checking your DNS Server is clear) or how frequently the DNS checks are done as my firewall doesn’t raise any flags.

I wouldn’t think disabling the Home Network Security would impact on this as in theory it is checking the home networks security (rather than external DNS. But I could be wrong.

You may find this helpful in the future for other info - the avastUI has a context sensitive help function - going to the area you are looking for some information and click the ? at the top right corner of the UI window.

I did this in the avastUI > Settings > Tools - which lists Home Network Security and clicked the ?
From the window that appears I found the “Home Network Security - Analyzes your home network for security risks. More…” The More… is clickable and produced the window (attached). This I would say confirms my suspicion that it doesn’t do the DNS checking.