Don't delete anything until we get some clear advice here, some of that could be actual OS stuff and we don't want to delete anything. Hopefully someone else will chime in.
What browser are you using? Try resetting it if it's Safari or clear all information if it's Firefox/Chrome. Is this happening at a specific website or all websites? Do you see these being downloaded?
Do the files have names indicating they are copies?
Example:
File.jpg
File-1.jpg means they are the same thing but two copies, which means they are being duplicated or downloaded multiple times.
Try this, go to Disk Utility in your Apps - Utilities folder.
Click on your Mac's main hard drive, the one with your OS on it, it will be listed in the left panel of the Disk Utility window that opens. Then click on Verify Disk Permissions in the bottom left. It will take a while. Let it run until it's done. If it finds anything that has incorrect permissions, click on Repair Permissions on the bottom left. Let it run until it's done.
I'm not sure what is going on but let's make sure the OS is working correctly before we do anything else.
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Do you have Aperture on your Mac? Do you use it to import photos from your camera?