Do I also get my State refund or is it included in my federal refund

Federal and state refunds are separate. They are processed differently. 

How come I can only see my federal income tax refund status but not my state refund tax?

Since they are processed differently, you will not be able to check the status of your state refund the same way that you would check the status of your federal refund. Here is a link on how to check the status of your state refund.
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