No, you do not need to do that. All steps will be processed completely online.
No, you are not permitted to apply in that case.
The Omani eVisa is not available to Diplomatic/Official Passport Holders. There is just only the ordinary passport is able to use for apply Omani eVisa.
The only requirement for your visa/residence permit to be used as a supporting document is that it should be still valid (by date) by the time you enter Oman.