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Both of those should be able to create a folder. Can you create one via your pc if you connect your phone?
No, I cant. I get an error saying the device has either stopped responding or been disconnected. Yet I can browse the files on it.
This is a 32GB Patriot Class 10 memory card.
File System says "Generic Hierarchical"
Should I try to format this card from Windows with a FAT32 or exfat filesystem then try it?
As funkylogic stated the 32GB card will not support exFat. I would move your stuff to the PC and Format the card using the Phone, then put your stuff back. Hope this helps.

Is this an issue with any 32GB memory card or is it this particular kind?
What issue were you referring to?
Not being able create folders on the SD card

Not being able create folders on the SD card
As funkylogic stated the 32GB card will not support exFat. I would move your stuff to the PC and Format the card using the Phone, then put your stuff back. Hope this helps.
As funkylogic stated the 32GB card will not support exFat. I would move your stuff to the PC and Format the card using the Phone, then put your stuff back. Hope this helps.
Do you have a spare card to try to determine if the card or the phone?
Yep. I think you may have a dodgy card, did you get it off Ebay, or a reputable dealer?