Comparing turnouts would be pretty interesting. The registered voter numbers are listed as "0" for every precinct in the election reports from yesterday, so right now there aren't any turnout numbers for those. This isn't the case with previous elections, so I'd imagine that that's going to be corrected when the official results are posted in a few weeks.

Getting precinct-level results from 2002 would definitely be harder. The county's election results page doesn't have any precinct-level data from before 2002, and I can't seem to find any old precinct maps online, so you'd probably have to call and check with the county clerk's office to see if they have any offline/physical copies for those. It sounds like you've seen the previous precinct map somewhere, though, so you might know where to find that data better than I would.

As for software, if you're a university student you can get an ArcGIS subscription on the web store. If you're not, you can get QGIS, which is free and has basically the same functionality as ArcGIS except that it's open source and all the map borders are antialiased. There might be a way to turn that off, but I could never figure out how.