Anonymous but not over https? Yes, you said you're gonna add it at some point, but it doesn't inspire much confidence. You should start with that.
Also, architecture? The about section doesn't say much. And you store messages(but not IPs) to what end?
There is obiously some security problems. ;)
How come you store the chat messages?
If it's "on your list somewhere", then change the name or put a huge disclaimer that says "it's not really anonymoys and it's a toy project".
You really have to describe the guarantees(if any) and what you mean by "anonymous". Anonymous as in "your mother won't know it's you"? Or anonymous in the sense of the post-snowden era?
e.g. can a whistleblower use this?
Is the code available? How does it compare to https://crypto.cat/ ?
I see you allow file uploads. How do you handle file storage, isn't that potentially expensive (DOSing your bank account)? And what about legal problems (copyright infringement and illegal stuff)?