This is interesting, because in XF's general forum permissions editing permission for a moderator does not include permission to reassign a post or change date and time.
Neither Threads, nor Posts have a reassign feature (nor a change dates feature), however, if they did, the XenForo Developers would develop those reassign features the same exact way as they developed the reassign resources for the XenForo Resource Manager (which is the standard that I follow for reassign functions in my add-ons). It would be a very easy customization for even a novice developer to write an addon for you that adds a new permission and extends the canReassign() permissions check to take that new permission into account. Contact Ozzy47, they are quick and cheap and know my addons.
1. I did not see that a change of owner or time was recorded in the history of the edited message. Is this an error on my part?
No, nothing you've done wrong. The Core XenForo Edit History Handler is only for the MESSAGE field, not anything else. There are several suggestions posted at XenForo.com to enhance the Edit History Handler.
I at least need to know which moderator reassigned and why.
When a piece of content (Article, Comment, Review) is reassigned, that is logged in the Moderator Logs (which can be viewed on the article itself or in the Moderator Logs in the Admin CP). The moderator can include a reason, however, that is only for the Alert that is sent to the Current Owner and the New Owner (again, 100% as XenForo developed it for the XenForo Resource Manager).
2. If in any case I want moderators to have the possibility to edit posts and comments on articles, but without the possibility to change owner or time, is this possible.
The editing of POSTS is a Core XenForo function, controlled by Core XenForo. Core XenForo does not have a reassign function, nor a change dates function for any of its content types (Threads, Posts, Conversations, Profile Posts, Profile Post Comments etc. The only reassign feature they've developed is for the XenForo Resource Manager.
As for AMS, if the viewing user can edit any Article or edit any Comment or edit any Review, they have permission to reassign as well as change dates. If the viewing user is a Contributor (author, co-author, contributor) for the Article and they have permission to edit the article, they can change dates.
It will require customization to do what you want to do. I am sure Ozzy47 can do it quick and at a very reasonable cost
