When it wants to write into XML it said: Error on line 8, position 3: Only one top level element is allowed in an XML document"
This is a result of either you DLL or EXE XML files being already corrupted before launching the GSX installer, which correctly check with Windows if the XML file is legal BEFORE trying to change it (if it didn't, the file would be easily corrupted even more), when a corrupted XML file is found, you are issued with the error, so the installation will not continue until you fix the errors.
If you don't know how to fix it, if you post the files ( ZIPPED, and Attached to a post ), I can tell you where the problem is. You don't say if you use FSX or P3D, so it's difficult to tell you exactly where to find the files, if you don't know it already.