Is there a way to open old (e.g. 2002) .tax files? If I try to open them in Turbotax 2016 the program dies.

Sorry no, that tax year is no longer supported so the program will not work and cannot be updated. 

You could try the TaxPrinter service at  http://www.taxprinter.com 

They might be expensive and it is probably not safe to email tax returns back and forth  Their Website says…….
We read most federal and state files (Windows and Macintosh) from years 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013... Known exceptions are TurboTax 1997 and TaxCut 2005 files which we can't read for technical reasons.

OR get a copy from the IRS - but I doubt they still have that year available. 
http://www.irs.gov/Individuals/Get-Transcript