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 residing on server as well.
2. If I want to keep mail locally but remove it from the server then I should create a personal file in Outlook. The personal file & any subfolders I create in Outlook are not replicated on the server. I can move mail from the Inbox or any of its subfolders in Outlook to a subfolder in the personal file and it will automatically be removed from the server. This is the best way for me to housekeep my email as I am the only person accessing them and only want to keep copies on my local machine.
Yes again. If you move the emails from Inbox to an offline pst file, they will be removed from server and stored locally. One disadvantage being the data risk as if the file gets corrupt, you might lose all your emails as they will no longer be on server. One remedy is to take backup of personal storage file after regular intervals.
3. When I delete mail in Outlook it is automatically deleted from the server as long as I have the account set to purge items when switching folders when online.
Yes, the mails are deleted from server as well whenever you have deleted them from outlook and it synchronizes emails with server.
Hope this helps.