The Influencer score is calculated across sitewide behavior. Therefore, it cannot be refined to determining the influencer in a particular group; thus that number being zero when scoped to a group.
I am unable to reproduce the issue you mention about where you go to the Dashboard > scope to a group > see zero influencers > scope to all groups > and still see zero influencers. When I am on the Dashboard and scope to a group, I see zero influencers (this is by design), when I scope to all groups, I do see more than zero influencers.
Power users are not based solely on influencers. There is a power users report which displays the top users in each of the user type categories. Only "influencer" is based on the influencer score, the other user types do not take it into account.