I wouldn’t address it in a cover letter. If it comes up in an interview, you can briefly address it, but anything in a cover letter is going to come across as you making excuses.
That said, I also wouldn’t wait to try to land a job. Start applying now and see what happens.
You may also want to see if your school has a mechanism for petitioning grades off your transcript. If so, it may be worth pursuing that.
I think this will always depend on the particular facts (and obviously I'm not offering advice here). But if it's a private conversation between members of the bar and your friend already knows you acted for someone in such and such matter, which is public knowledge in any event, and all he's asking for is general guidance, then I don't think it would be unusual to discuss what kinds of things the court was looking for, what worked and what didn't, things to avoid, etc. You wouldn't disclose the reason why you did or didn't appeal or anything that would reveal the content of privileged conversations. But giving general guidance to a colleague to better the expertise of the bar is, I think, different from disclosing to a non-lawyer or the public and since you're the lawyer it's your own ass on the line (rather than an employee risking your ass for you by their own indiscretion).
That said, I don't know that I'm often in that precise situation. Normally, if I'm discussing with a friend about a case in the way you mention, it's without knowledge or disclosure of names or other identifying information.