Iphone back up problem

I am going to do this in step to step of what happen so it makes it more legible.
And make sure it is nice and simple so please help if you can!

1)I installed a craked version of IOS7
2) I changed time to a different country
3)It froze
4) I had to plug into my MAC in to itunes
5) Make it DFU mode
6) Tried to reinstall to IOS7 to get the back up (because it is a newer version of OS so I cannot put the back up into the IOS6)
7) When it is in recovery mode it only let me 'RESTORE' not 'look for updates'
8) So it says I am not a developer so i had to reinstall back to ios6
9) Here was my plan, it was to go back to ios6 and the 'back up' is still there but it require ios7 to install
10) So i decided to press 'set up as new iphone' on itunes to get to the page where there is an option for 'look for updates'
11) I knew this could over write my wanted 'back up' so i went into the itunes library and copied the 'actual' back up folder the one which have lots of random letters and numbers (in the attached section)
12) When I press 'Set up as new iphone' it did overwrite my wanted 'back up'
13) I tried to put my backup back to the library folder but the 'back up' does not show up on itunes
14) I lost all my documents, photos and settings

So my questions are:
1) If i reinstall ios7 will the 'back up' show up in the itunes library? (in the part which says install from back up)
2) If not, are there any way the make the 'folder back up' show on itunes?

Thanks alot any helpful answers and suggestions are greatly appreciated!

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