You go the error in fragmotion because fragmotion doesn't actually import most FBX formats, it worked ages ago for a few types of FBX, but it hasn't been updated since and no longer fully supports FBX. That's the problem with FBX, and why Lee's had trouble implementing it, there's so many versions of it out there by the time you get your import software working there's a newer version and oyu have to start again, so if you're not a major publisher with a team dedicated to just working on the importer you have your job cut out for you.
As to later versions of blender having issues exporting, as far as i know that was one version about a year ago that was fixed in the next version (i broke sometime in 2.6x and was fixed sometime in 2.7x i think).
When exporting as .x did you make sure both the skeleton and the mesh were selected? They're separate objects and both need to be selected at the same time during export.
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