Can I file my State return due on 6/15/20 and wait until 7/15/20 to file the federal return?

You can't efile state until federal has been accepted.

You can file state before Federal but you have to mail state.

https://ttlc.intuit.com/community/e-file/help/can-i-e-file-my-state-return-before-my-federal/00/25545

You have to first fill out federal for it to flow to state and pay the fees for both by credit card.