I am very new to sublime. Never written a plugin before.

Each line in the file , to have the full path and filename.

Is there a plugin or way I can get sublime to maintain such a text file of open text files?

So it appends to the list of open text files when a new one is opened, it removes the filename from the list of text files when it is closed.

You could write a plugin to do this. Check out on_load and on_close.