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Does it have the little slider like the
old floppies used to have? Maybe
it was moved into the read only
position accidentally.

As to the read-only flag: You're looking at the read-only attribute
for the root directory. But there is no read-only attribute for a
directory. What you're seeing is a shortcut to allow you to set or
clear the attribute for all files in the directory.

Each time you display this tab of the properties dialog, you're
looking at a 3-state box in its third state: neither set nor unset. On
my computer that shows as a green blob in the box. Click it once, and
the box is empty, that's the NO state. Click it again and a check
appears, that's the YES state. If you click OK or Apply when the box
is in the YES or NO state, the read-only attribute is set or cleared
(depending on whether you're in YES or NO state) for EVERY file in the
directory. But when you bring the box up again, you will again see it
in the third state.

If you bring up the same box for the individual files, you'll see the
result of what you've done.

No, I don't. You've said that the r-o slider on the side of the thumb
drive is positioned correctly, besides that you can create new folders
and files. I can only guess the hardware (the thumb drive) isn't
working properly.