Why does my turbotax fees have the turbotax federal fee taking out $60 an the TurboTax State fee taking out $45 from my refund?

It sounds like you added Refund Processing Service to your cart, which is the option to pay to have your TurboTax fees taken out of your refund. I'm including details on this service below for reference. 

https://ttlc.intuit.com/replies/3301372