A very long time ago, years, there used to be a statistics element were it used to show the last 5 files scanned, this has been dropped by Avast.
Personally I never considered it of any particular use to me, as in effect it was historic, by the time the data was displayed it was out of date (and insufficient) it would have been scanning. But some others did and it was muted that a Statistics section, it was muted that it would be revamped, but so far it has never come back.
Have you thought that something like you mention would also be generating CPU and RAM activity ?
Surely the Task Manager would give a better indication of Avasts activity, in regard to your first and this latest question (CPU and RAM usage) ?
Avast is always going to be monitoring your activity (it what on-access antiviruses do) depending on the Shields that you have enabled, File, Web, Mail Shields, etc.