I don't know anything about iClone, but I would assume the FBX files should work if you can import FBX models with animations. Based on what I see online about the "no compatible avatar for conversion" error, iClone can't recognize the rig. try checking to see if the imported model is imported as a prop or a custom mesh instead of a Humanoid Character, then you need to set the bones to the right place in the settings, if it's being imported by going to File > Import, then you need to Import as Character / Humanoid. if you are using the meshless(No Mesh File) file try the Anima file and see if that works. As for the refund you have to ask for a refund, by asking Itch.io's support team.
Detailed instructions on the no compatible avatar for conversion error fix:
Select the mesh, go to the Modify Panel, and look for Convert to Character. The most reliable route is to open the FBX file in Character Creator (CC4), select Humanoid, and use the Characterization tool to quickly map the bones. Once mapped, click Send to iClone and retry applying the animations.