Syncing drafts sounds like a reasonable expectation (I thought it was already done?).
Why would I want to go to the first message within a year-old chat with thousands of messages?
Navigating it through some kind of a calendar widget would be nice, though, but that’d be a different feature proposal. I.e,. similarly to what you get on the chat logs of IRC & XMPP servers - you could go through years, months, and it would show days that had messages (even the count per day), and clicking on a day would jump to the first message that day. It would look even nicer if combined with search.