If you want to read the answers, just click through to the question. Then go back and review.
On a site with review audits enabled, this is worth doing in any case because you'll never get stung by a bad audit if you first have a look at the actual question and answers.
1. Head to Edit profile and settings.
2. Find "Navigation" in "Preferences".
3. Find "Hide left navigation (When you check this box, the left navigation will no longer be pinned to the left of the page on Q&A sites.)" in "Navigation".
4. Hit it!
6. Profit! If anything failed, go back to step 5 and try again.
If I bring up the selection box for reasons, I rarely find a near match to the problem.
You don't have to use one of the canned comments; you can go to the Q&A page itself and leave a more applicable comment. (Or use one of the comments and modify it, if that's easier.) There's a handy 'link' to the post:
From there, you can also do something about the ...
The phrase you quoted from the review page simply means that as users with enough rep to have the privilege to review, we help to moderate the site by reviewing items in our review queue.
It is not meant to imply that we are moderators, as in the sense of elected or pro tem moderators.
My experience, and others too, is that reflagging does nothing
Well, if your intention is to send it to the Low Quality Posts review queue again, that certainly won't happen, according to this answer by Shog9:
Once reviewed, further flags do not re-add the post to the queue. At this point, a moderator will need to intervene. These flags will continue to ...
The kerfuffle appears to be about moderators questioning a new CoC that they had been shown.
It would be entirely unreasonable for ordinary users to be suspended for violating a new CoC that they have not been shown.
Obviously, don't be a jerk, but that's a sensible recommendation all the time :-)
And there appears to exist some private and/or confidential information, available only to moderators
There is no private or confidential information that I've seen (moderator on SO) which would indicate it's unsafe to continue reviewing. There is, in my opinion, no danger to yourself or your accounts in doing so.