No it does not upgrade automatically. When new updates arrive on Itch.io, you gonna need to download the new update and replace your old folder with the new one.
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Your saves is in the registry, so it does not get deleted when you remove the folder. To locate your saves, you gonna need to use the Registry Editor, then find it at HKEY_CURRENT_USER/SOFTWARE/Fatal Fire Studio/FAP NIGHTS AT FRENNIs.
For further information on how to transfer saves to a new device, I suggest you ask on their Discord.