Turbotax 2013 will not recognize *.tax2015. How do I import/convert *.tax2015 to *.tax2013? Or otherwise import or save 2015 Turbotax data to use in Turbotax 2013?

You can't go backwards.  Why do you want to?

Each year Turbotax program can only read and edit it's own files.  It can also import the previous year only, to use as a starting point for the current year, but it can't read or edit the previous year.

Thanks.  It's an educational exercise to decide whether to amend previous years.  The data is not real.  No return was ever filed or ever will be.  Unfortunately, I started with 2015 instead of 2013 and have to re-enter everything.

Not possible.  You cannot transfer a 2015 tax data file to the 2013 desktop edition tax return.  Only prior year tax data files can be transferred to the current year software, ie 2014 to 2015, 2015 to 2016, etc.
And only the the tax data file for tax year 2013 can be opened with the 2013 software.

and if your due a refund for years prior to 2016, forget it.  the statute of limitations for claiming a refund for those years has expired.   however, if you owe, because you have never filed the IRS can go after you.