Hello Russell,
Be sure that we all have been there and know the feeling; that's why we try to share what we have learned in the process, but cross-posting only adds to chaos in several ways, for example, 1) people sometimes miss track of their own duplicate threads, and so they may be unaware that some might have already been answered; 2) someone may find a post, unaware of the fact that it is a duplicate post, spend what could be a considerable amount to answer it, only to find that the issue has already been answered or solved in another post; not a good thing, believe me.
As I recommended, next time try to just let things flow; if it is very very important and the post hasn't been answered after a day you may bump it (not open a new thread). However, do take into account the following possibilities for a post not being answered as fast as one would like:
1. Sometimes posts aren't quite clear or lack enough information, and while usually someone takes time to alert the poster about that, it can also happen that the post goes unattended.
2. The issue in question could be relatively complex and so, maybe someone has seen the post and is already doing tests before answering at all (as a side note, at least I tend to do that).
3. The issue is relatively simple and/or has been answered uncountable times and so it could be solved if the poster took time to either:
a) Read the corresponding documentation:
http://docs.moodle.org/27/en/Main_page
http://docs.moodle.org/27/en/Table_of_Contents
http://docs.moodle.org/27/en/MoodleDocs:Overview
http://docs.moodle.org/dev/Main_Page
b) Search the Moodle site:
https://moodle.org/public/search/
c) Use the forum search option.
d) Use an Internet search engine like DuckDuckGo, StartPage, Google or any other.
One last comment regarding duplicate posts; when one is created, it usually is reported so it can be deleted before it is answered and so help keep the forums relatively organized and structured.
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Now, regarding the several issues you have, as far as I could understand:
1. All seemed to start because of double clicking when saving. Various answers given here:
https://moodle.org/mod/forum/discuss.php?d=266002#p1151157
a) Don't double click.
b) Fix it ideas:
** Delete the duplicate questions from your quiz bank (same answer here: they have never been added to a quiz).
http://docs.moodle.org/dev/Quiz_database_structure
http://docs.moodle.org/27/en/Verify_Database_Schema
http://docs.moodle.org/27/en/Quiz_FAQ
http://docs.moodle.org/dev/Question_database_structure
http://docs.moodle.org/27/en/Quiz_module
** Database connection might be timing out. Check your mysql settings and increase the timeouts.
https://dev.mysql.com/doc/refman/5.5/en/mysql-options.html
https://duckduckgo.com/?q=change+mysql+connection+timeout+setting
http://docs.moodle.org/27/en/Administration_FAQ#How_to_change_the_maximum_execution_time
** Or your backup might be corrupted. Fix the previous errors and retry.
2. You have some strange questions that can't be deleted. See previous point.
3. You say that you have a backup problem... and a similar problem with import.
Here you seem to be unclear or aren't keeping the issues focused. Marcus was answering precisely about that:
https://moodle.org/mod/forum/discuss.php?d=264831#p1147941
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If you are about to work directly with the database, please do a site backup before and do check that it is a functional backup (i.e. that it can be restored):
http://docs.moodle.org/27/en/Site_backup
Have you tried exporting the questions and working with the exported file instead?
http://docs.moodle.org/27/en/Export_questions
http://docs.moodle.org/27/en/Import_questions
http://docs.moodle.org/27/en/Questions
http://docs.moodle.org/27/en/Managing_questions
http://docs.moodle.org/27/en/Moodle_XML_format
http://docs.moodle.org/27/en/GIFT_format
Cheers!