So I have taken screen shots of what C++ redists are installed.
I'm sorry, but that screenshot is not very helpful, because it only indicates how many products can be Uninstalled, it doesn't say anything if they are installed correctly, not corrupted or not conflicting against each other.
I too have VC++ 2010 installed, and there are no problems with it. In any case, the Couatl.exe (version 3) requires the VC++ 2013 by itself, and in inherits a dependency on VC++2005 because it uses Simconnect (which requires the 2005 runtimes, likes FSX) so, in *theory* it shouldn't be affected by the VC++ 2010 runtimes.
All installations were run without Anti-Virus (Norton) and as "Run As Administrator".
Something must have happened at some time, because your error really means the executable image format is "invalid", which really looks like a corruption caused by the antivirus. As I've said, you can check this, if you go to the P3D\fsdreamteam\Couatl\Couatl.exe file, right-click on it, select "Properties", select "Digital Signature" and check if the signature is valid. If it's not, then it's SURE it's antivirus which has corrupted the file trying to "heal" it.
In addition to that, there's no difference whatsoever regardless if you have P3D 2.5 or P3D 2.4, when Couatl is concerned. Couatl doesn't even KNOW what P3D version you are using, surely it doesn't know (and doesn't care) about the difference between 2.4 and 2.5, the only think it needs to know, if it's FSX, P3D 1.x or P3D 2.x, in order to know where to look for the scenery.cfg, but that's it.
So, whatever difference you see running under P3D 2.4 or 2.5, cannot possibly be related to the Couatl program itself, since there isn't a single line in its code that ever knows the difference between the builds. The only program that checks the build and needs to recognized it, it's the Addon Manager.
BTW, the Addon Manager also require VC++ 2013 and 2005 (because of Simconnect) so, if THAT one runs, it seems to indicate there's nothing wrong with your VC++ libraries, and the issue is ( as usual ) the defective Norton.