No, you are required to have your Oman visa before your trip to Oman. 

The visa fee will be mentioned in US dollars and you will have to pay through PayPal, credit or debit card so you don't have to worry about the type of currency. 

The usually processing time takes 4-7 days. However, you can also get your visa processed with express processing which takes 24-48 hours, urgent processing which takes 7-8 hours or super urgent processing which takes 3-4 hours. 

It is not mandatory. However, you can carry it with you in case you are required to provide it. 

If you intend to extend your stay in Oman, you can apply for 30 days visa extension.