Now, I did a cursory check of the todo list and feature request list, and I didn't see any of these there, but sorry if I just missed them. I also want to say that this is all from my limited experience and in my opinion. I have no real knowledge of coding, and only rudimentary knowledge of diplomacy, compared to many of you.
So, onto the suggestions:

First, I think adding voice chats and/or voice group chats would be fun.
I mostly play live games since I am on medical leave from school and so have a lot of free time on my hands, and I find them more intence. I was thinking, and I believe one of the big attractions to live games (for me at least) is that they are closer to my (very limited. Two to date) experience of face to face games, mostly because they are faster, more intense, and you end up getting into more of a conversation with opponents, instead of the dipping being Iike pinning a message onto someones door and waiting for a return letter. Not that I dislike slower games, I just like live games and FTF games better.
So I was thinking about why I like live and FTF gsms better, and I decided that as much as it being the fact that things feel faster and more intense, it was also the feeling of talking with other people. This suggestion would mostly be good for live games, but I think would also work for the instances in non anon games when two or more players are both on at the same time and talking.
(sorry for the ramble)

Second, I think having a friends list and a way of searching for a user might be nice.
I think this would make more of a community because you could talk with people while not in games together and without cluttering the forum, and I also think it would make it easier to get high quality games together where people won't CD. One of the reasons I have seen discussed, and something I though made sense, for why the cd rates are so high, is the lack of sense of consequence and lack of sense of responsibility many people seem to have. By making it so that you can add people to a friends list and maybe even an avoid list, I feel like it would help the people interested in good games of diplomacy with quality players have an easier time finding a game with people who aren't going to cd. Also, it would make it easy for players to easily organize themselves into mini leagues, which could add an interesting/fun aspect to the community. I understand this might increase metagaming in some respects, but I think so long as the game is all from your friends list or you are all rule respecting players, it shouldn't be too bad.