Hi,
1. Yes, TF uses the elevations provided by the GPS itself. It can also use elevations along the route, as you say, if you have DEM data for the given area. You have to use the 'climbing analysis' box to add DEM elevation to the file. DEM elevation also has its problems, btw.
2. It is likely that you lost signal at some point during the run. The GPS didn't pick up this distance since it had no signal, but then you used TF to merge the segments together resulting in a longer distance. The TF is probably closer to the actual distance you ran.