I had to fix something and re-file, will I get billed again?

No. 

You will not be charged again to re-file a rejected return.  You are also never charged again for amended returns if you were to need to amend your return.

I filed my taxes using free federal turbotax online and payed for the state filing. Both filing was rejected and I had to pay again to fix and resend. Is this double payment for the same service correct?

I