I downloaded a lot of cc 2 days ago, and as it was taking a long time to individually click on them in the launcher, I just clicked install all. (I already have a lot of cc)
I noticed in my downloads folder, that i had some cc in tmp folders and a few others, which have never shown in my game. So i moved them from the folders and placed into the main Downloads Folder. I then installed them in the launcher.

Since then, my game will not load. It just goes to a blank screen and a blue circle going round.
When i looked at the launcher, all my Downloads were not showing, or installed content.
But they're all still in the downloads folder.

I don't know what's happened. Have i made it unstable by moving files out of these subfolders?
How can i get it to work again?

I will start you off with "next time"... Many, including me, will convert sims3packs to packages using this tool. Use a framework set up that has a "test" folder, and always put new packages there first, making them easy to remove, or perhaps do a 50/50.

Now, sounds like bad cc. Hopefully someone who is 100% sure will pop in, but I believe launcher installed cc goes into DCCache folder. Do not delete, but move everything in that folder to another folder outside of your Sims 3 main folder and try starting the game. You can always put everything back later. If the game starts, great. After that, it will be patience and installing only a few items at a time and checking, OR convert to packages and use a test folder.

I moved the contents of the dccache folder, and the game loaded. So I guess I'll have to put a few downloads back in at a time and test it

I would use the tool I linked and convert to packages, and use framework that supports a test folder. I use it for everything except worlds. You can put all of the sims3packs in a folder and convert all of them in one shot. Be sure to check "rename files", or you get package names like the ones in Library folder.

Drop 10 or 20 into the test folder to be sure the game starts and runs. If no, remove those and add in 10 other. The broken one may have been in the first batch. Also, get Sims3 dashboard tool. It's on MTS. It will check conflicts and duplicates, or if you accidentally installed TS2 or TS4 packages, which will break your game. I run that tool every time I add anything.