With several addresses configured on Thunderbird it always stutters the first minutes of using it until all new mails are downloaded. This issue does not seem to be fixed and at least for me would bring more benefit instead of a redefined GUI.
Never happened to me, with several IMAP accounts. Are you using pop3 maybe?
No only IMAP. But I have 3 accounts which download each day around 300 log e-mails.
I recently turned off the global indexing and it has improved performance immensely. I actually don't use that search that much so I'm going to try it without for a while and see how I go with the basic search stuff.