On your #1 issue: it’s a well-known and acknowledged problem. Basically, the current Thunderbird doesn’t have unique message IDs across folders, which causes issues when displaying messages from different folders in threaded view. One of the common workarounds involves making copies of Sent messages in other folders like INBOX.

There’s a major internal message storage rework project happening in Thunderbird, which should fix this once completed. You can try it in some beta builds, but of course, it’s still beta and isn’t compatible with some plugins yet. Most notably, the TBSync plugin, which provides Microsoft Outlook integration, doesn’t support it at this stage.