One small fix suggestion regarding shrink or expanding the header. (...)
Nice one! The patch is
here.

Something related to persistence: the
Post a redirection topic checkbox from the Move Topic page should be disabled by default. Redirection topics left by members are seldom useful and mods leave them sporadically. Having the choice saved would be a small benefit.
Albeit it's more useful for mods when moving lots of threads (had a userscript long time ago disabling the checkbox to save some mouse travel and clicks

).
For example, I may not be looking for any particular conversation I've had with user X, but I want to get all the messages we exchanged.
I'm currently working on something that'll help with that. If what I have in mind doesn't end up solving your problem, then I'll re-visit your specific suggestion.
Another feedback: When searching for PM, I want to be able to search to my Outbox only, instead of my Inbox.
Yup, it's on my list (it originally came to me from Cyrus).
Thanks for putting that on your list! IMO it's an easy way to a sort of faux conversation style PMs by having the ability to show all messages to and from a certain user without needing to search for a keyword (there's always that off chance you might miss a PM because it didn't contain that common character you used to search for

).