Thank you very much! Now the issue is solved!
#13 did not work because the eye was already open.
#14 worked. Basically I did not see "administration" in the Add A Block list previously. It took a long time to realise but now I understand that unlocking the padlock icon for the administration block in the "Manage Block" page brings back "administration" in the Add A Block list. As soon as I lock the padlock, it disappears, so I have to keep the lock open while I add the administration blocks to pages.
With regard to the front page, I was still not able to add the administration block back because there was no way to turn editing on and so was not able to use the "Add A Block".
So, I did the following
1. Keep the padlock unlocked for the administration block in the Manage Block page.
2. Go to a course page and turn editing on.
3. in the url box in my web browser, I typed in the front page address.
4. Now I was back in the front page with the editing mode on. So, I found the Add A Block.
5. Add "Administration" block using the Add A Block in the front page.
The issue is solved, but, I still think that moodle should make this much easier. First of all, the administration block should not be deleted so easily from the front page. If it is deleted, there should be much easier way to bring it back. Moodle is rather a complicated system to get around for non-technical teachers and users..it is my opinion at least.
Anyway, thank you very much for your help.