Can i efile federal and state at different times

You should have no problem.  Just check the circle for efile federal and check the circle for I'll file state later (or vice versa).  When you're ready to file the other just go in and check the other box.  It should work.

Yes, you can e-file your federal return by itself first.  However, you cannot e-file you state return before the federal.

Because of the number of fraudulent state returns submitted in the past, filing the state return by itself is only allowed once a federal return has been accepted.  Once you receive notice that your federal return has been accepted you can go back into TurboTax and e-file your state return.