If the current QAT (you can define several) is selected from the Enterprise CUIx, it cannot be modified. Ensure yours is defined in the Main CUIx.
You should be able to rt click on any command on Ribbon and select "Add to Quick Access Toolbar".
According to help you should also be able to drag commands.
Right-click method works fine for me.
Drag+drop not so much. I could drag+drop a command, but not on the very end of the QAT, so I dropped it in the middle thinking I could move it over with another drag movement. No, it wouldn't budge. Then I shut down and restarted and it was gone. Strange behavior.
It might not be possible to add CLOSE to the Quick Access Toolbar, at least not using the "Add to Quick Access Toolbar" method.
2 alternatives I use often which you may find to be just as quick are:
CTRL+Q = Close.
Clicking on red X on upper right of drawing window area.
My intent is to insert a simple "close" button to the QAT.
I just did it in less than a minute.
Now having said that, I would never use this button since there is always a document level "X" available to close the current drawing.