What I noticed though is, that it gets installed into this folder: F:\FSDT\Addon Manager\Addon Manager
It's installed there because you chose to install there so, it's seem the first time you chose the F:\FSDT folder, so it installed into F:\FSDT\Addon Manager, which is normal, but then you somehow managed to bypass the lock the prevents you to re-select the previously installed folder again, which is there precisely to prevent you to do the mistake of installing one product into a folder and another into another one so, the 2d time you chose F:\FSDT\Addon Manager, so it installed into F:\FSDT\Addon Manager\Addon Manager.
I have no idea why you manage to change the installation folder the 2nd time because, as you might have noticed, you are only allowed to choose the folder freely once, then it default to the first choice.
Of course, if you created an F:\FSDT\Addon Manager\ folder manually, and installed there, it's entirely normal that it would install into F:\FSDT\Addon Manager\Addon Manager, which is not really a *problem* as such, you can install anywhere, it's just not very nice to look at.
In any case, to "undo" your choice and be able to select the folder freely again, you must uninstall everything, and at the end, reply YES to the question "Do you want to remove the Addon Manager?", so your initial choice will be cleared up and you will be able to choose the folder freely on the next installation