Is my federal refund include my state with it?

No.  Your federal refund and state refund are separate.  They will come from separate entities when they are issued.  They will not arrive together.

I made a mistake when I filed my federal return, the irs reviewed the errors and fixed it and sent my federal tax refund out but didn’t tell me how much state tax I would be getting back. Is there a way for me to check how much I get back with the state ?

Federal and state are completely separate.  Unless the state sends you a letter and changes your state return you will get the original state refund.