On the IM side of things, you should check out OTR (off-the-record messaging): https://otr.cypherpunks.ca/ - in particular check out the top 4 goals mentioned on that page.
The keys are effectively public once the conversation ends -- they aren't tied to your identity. So those messages could have been forged by anyone, there's no proof they came from you.
However, I don't quite understand how "anyone can forge messages after the conversation" works. Can you explain any more?