I want a report that shows:
* A list of languages showing the users who speak each language as identified on their user pages
* A list of projects where users have made at least 5 edits in the past 12 months
* A list of group members that have administrator rights and which wikis are involved
* A list of public mailing lists where members have contributed in the past 12 months 
* Number of public emails on those mailing lists in the past 12 months

What Oliver said for these questions
 
* Total edits made by the cohort
* Total bytes changed by the cohort

For these, you could use Wikimetrics: https://metrics.wmflabs.org/.  We have Edits and Bytes Added metrics which you can run on any cohort.  Cohorts consist of lists of users in specific projects.  So it wouldn't be able to go across projects for you (yet, we're working on that) but you could upload a cohort that has each user you care about in each project you care about.  Also, we're adding new metrics soon.
 
* Total logged-in time for the cohort, if log-in time aggregation is being done

Same as above, see Oliver's answer

Are there any significant editor productivity metrics that are missing from this list?

We're adding a few new metrics to Wikimetrics but Survival, Pages Created, and Threshold are also available right now.  I wouldn't say those are "significant productivity metrics" but they're something to get started.  The new metrics we're implementing aim to be more along the lines of what you're looking for.  You can see that work here: https://meta.wikimedia.org/wiki/Research:Metrics_standardization and specifically we're going to be adding these four metrics within the next few sprints:

https://meta.wikimedia.org/wiki/Research:Newly_registered_user
https://meta.wikimedia.org/wiki/Research:New_editor
https://meta.wikimedia.org/wiki/Research:Productive_new_editor
https://meta.wikimedia.org/wiki/Research:Surviving_new_editor

Hope that helps and check out the Wikimetrics support page for more info.