An app would... not necessarily eliminate any of that. :-/ And you'll have to take my word for it, but adding an app as well would probably nearly double the amount of code required to maintain, unless the app was a very very thin veneer over the website (as in, an app that says "here's a webkit browser view, locked to webdiplomacy.net), in which case... you might as well just go to the website.
Also, you'll probably just have to take my word for this too, but you would probably not believe how ugly it is, debugging and fixing the tangled mess that is javascript vs html vs server script issues. Web browsers all implement javascript slightly differently, and getting access debug javascript issues at all, especially on mobile browsers, is really really painfully annoying. :-/