I am not sure this will help but:
I have an imac using an external usb superdrive, the drive does not show up on my desktop but I can still burn to it.
I right click on the folder I want to burn and in that menu it says, burn “name of folder” to Disc, click on this and it will burn to the cd/dvd. Once it has finished the icon appears on my desktop and is readable.
As far as ejecting the disc I use the key in the upper right corner with the triangle and line under it, next to F12 and that works for me. (on my keyboard)