My thoughts, for what little they're worth:
1. Should DART moderation be able to punish users for sever misconduct which occurs on the site's discord?
Yes.
We should be clear that we are only talking about moderating punishing people for conduct on the discord for this particular site, which are only a function/platform derivative of DebateArt itself and were not utilized to the same extent that they are now on Debate.org.
This should be distinguished from Hangouts, which is not necessarily derivitave of DebateArt, as many of the same links co-exist on Debate.org, and Debate.org's Hangouts predated DebateArt.
2. Should there be a public ban log?
No.
I can see no added utility to this and it would almost certainly delegitimize any ban or other moderator decision; which would create more controversy, and risks creating greater problems in itself than any ban would be intended to solve.
3. Should COC-violating conduct be deleted?
The problem with this question is that there are many kinds of COC-Violating conduct; which cannot be appropriately addressed in a unidimensional way. The so called "MEEP" process should differentiate between different kinds of COC violations, of which there are at least several: spam, personal insults, posting private information, pornography, etc.
This question is insufficiently precise. No policy which could result from its answer would be good.