Hi
@PollyannaSims, welcome to active forum life
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a) The files on the D drive are the main game files and look fine. If the game runs then all is good.
b & c) The short answer is no, sorry. The files on the C drive hold the working data on the families and neighbourhoods that you have been playing. The game will always look for them there so if you move them it will re-create all the files and folders as if the game was newly installed. If you move the Mods folder the game will create a new empty copy and run with no mods.
If you want to back them up, copy them to a different location. You want to backup Saves (at least), Mods (if you have any), Screenshots, Tray (holds lots and houses you've made and any downloaded from gallery/web), Recorded Videos I think holds any in game vids you have shot so back that up as well if you need to.
In the folder on the C drive you will see a file called 'localthumbcache.package'. Delete this regularly to prevent glitches and crashes. I know Playalot deletes this file after every gaming session to prevent problems. I delete it when I remember.
Hope this answers your questions, have fun gaming.