Lol, Spoiler, you posted before me again.
This is what I was going to post:
But is it not so that when the disk is not full, new files can be added?
Nope. As long as you add data do the CD-R, it is write protected and cannot be written on anymore.
If you write something to a CD-RW, you have to format the CD and then you can write your files again.
Secondly, as its status of write protected has effectively stopped access or any other function, can this be overcome?
If you mean add more data to an already-burnt CD-R, I don't think this is possible.
Thirdly, just how do some CD-R disks come up with that status and others do not?
Not sure. Are you sure you aren't getting CD-R's and RW's mixed up?
More info on this would help us answer the question.
Lastly, how does one get rid of it so it is not write protected?
Like I said, it will need to be a CD-RW, unless you mean something else..
Hope that helped.