2) Should those actions be included in the new per-moderatorDefinitely yes.
1) Should I add those as notifications that group members can sendI'd generally say no, except add/modify photo album. And as mentioned before, for those that don't post I'd like the member whose content is affected (including deletes) to receive an off-list notice.
... I will add 2 per-subscriber notifications: notifications whenThis one probably needs two options: notify me of any like, and notify me of a like on my content.
Given that Likes are intended as light-weight alternatives to "me too" postings, we can expect (hope?) that there would be a lot of them. This one is probably the poster child for aggregating notices.
and notifications when someone posts to a chat their subscribed to,That's a good idea you have they're.