re:When I use Subscribe/Unsubscribe method and uncheck the folder it disappears from account folder tree. That is correct because you have just unsubscribed from seeing the folder.

All imap accounts are like a virtual view of what is on server, so you can manipluate emails on the server by moving emails between server folders.

Any folder in an imap mail account is also on server and you subscribe to see that folder. All imap folders synchronise with server to show what is on server.

Do not assume that any imap folder is storing emails on your computer. You may have chosen to download full copies of emails instead of headers, but as the folders constantly synchronise with server, the contents can be changed.

eg: If you delete an email via webmail account or another imap device like a phone, when you start Thunderbird, that email will auto be deleted because it is no longer in the server folder.

re: I want to move old messaged from Inbox/Sent folder to a custom created folder and exclude that folder from mail server synchronization. Then you must download full copy of email and store it outside of the imap mail account. In your 'Local Folders' mail account, create a suitable folder and put a copy of the email in that folder.

Thank you for explanation. That helped me a lot!!