Answers to your queries are as follows:
1. If I create sub folders in Outlook below the inbox then these folders will be replicated on the server. Any mail I move to these folders in Outlook will remain on the server.
Yes, indeed the emails moved in IMAP folders below Inbox will be...
Have you tried rebuilding the database?
https://support.microsoft.com/kb/2360509
Ensure you have enough space and memory on system. Depending upon database size, it might take time.