Is there a way to request multiple years of federal and state tax returns? (I need the past three years of federal and state). Is there an option to have it mailed to me?

Only you have access to your account   so save PDF copies of all 3 years to your computer then download them to a thumb drive and hand it to the CPA. 

I DO NOT HAVE A PRINTER—WHAT CAN I DO?

We cannot solve your printer problem for you  TurboTax cannot print it for you.   If you do not have a working printer,  you can access your account from any computer that has internet access and print your return. Or save it to a flash drive.   Perhaps you need to see if a friend or relative can let you print from a computer with a printer.  Or print it at a UPS place or Staples, etc.  

Have the CPA access the TT online account while you are in the office and let them download the files.