Many GPS devices come with their own mapping / editing software that may or may not be sufficient for your own analysis. Personally, I use Matlab for much of my processing b/c I have a lot of control, but you'll also have to do a bit of programming.
First, if you want to convert your file from your specific file type to .gpx (or vice versa), I suggest using GPS Babel.
For some editing / analysis, you can use Excel. Open Excel then open the .gpx file. I would open it as "read only" or "xml-source" which seems to disable the macros. From here, you can plot / analysis the columns of data, including latitude, longitude, altitude, and time. However I don't think you'll be able to save it back as a .gpx file.
The easiest way is to download the free GPX Editor. Open up a .gpx file inside, and select the specific track segment you wish to edit. While I have not checked out all the options, I know you can double click on a row and edit the information inside. Make sure you hit the "check" box or it won't save the change.