Can I save state return to disk and to computer? How? This part of TurboTax is not user friendly!

The state return is included in the pdf file.  You can't just download and save the state by itself.  

You should always save both the PDF file and the tax data file each year so you have a copy when you need it or if you ever need to amend it in the future.  You shouldn't rely on getting a copy from Turbo Tax.

Save the PDF

https://ttlc.intuit.com/community/saving/help/how-do-i-save-my-turbotax-online-return-as-a-pdf/00/26234

Tax returns created with the TurboTax online editions can saved as a PDF and/or a Tax Data File.

To access your current or prior year online tax returns sign onto the TurboTax website with the userID you used to create the account - https://myturbotax.intuit.com/

Scroll down to the bottom of the screen and on the section Your tax returns & documents click on Show.  Click on the Year and Click on Download/print return (PDF) or Download .tax file