When you say that your computer reads 0 free space, do you mean your PC says that when you plug it in using the USB cable? Have you umounted your SD card from your phone?
When you want to get into the files on the card while keeping it in your phone, you have to "mount" it. To do that, plug your phone into your computer with the USB cable. Then look at your android device. You should see a USB symbol at the top left of your phone (assuming you have a stock Android OS.) Pull the top menu down, and click on the area that says "USB connected." It will ask you to mount or unmount. Mount it if you want to do stuff on the SDcard.
When you are done doing stuff on the SD card, unmount it, and you should be good to go again. If the SD card is still full, then delete some files.
I hope that helps. Let us know if you need more help. I am not knowledgeable in Samsung's variant of Android, so I'm kind of guessing.
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