How to locate all iTunes libraries and condense into one?

Why do you need to add all backups? Surely the most recent one is sufficient. You can see if there are commercial utilities to merge libraries without creating duplicates as the standard procedure of simply adding media from one library to another will likely create many duplicates.

While re-installing the operating system should leave your other files unaffected there is no guarantee it won't, and re-installing the operating system does not actively include any feature to back up those files first. Re-installing the operating system is rarely necessary on a Mac (I haven't changed or re-installed my OS on this computer since 2007) but tends to be a behavioral carry-over from people who used to use Windows. If there are problems on a Mac it is usually best to address those specifically.

06/2014 ChrisCA post: Restore iTunes library from Time Machine backup - https://discussions.apple.com/thread/6374283?answerId=26104480022#26104480022 Useful tips where restoring to a new drive: http://pondini.org/TM/B6.html and https://discussions.apple.com/thread/6811322?answerId=27599985022#27599985022

No, a library is a bunch of files working together:

What are the iTunes library files? - http://support.apple.com/kb/HT1660

More on iTunes library files and what they do - http://en.wikipedia.org/wiki/ITunes#Media_management

What are all those iTunes files? - http://www.macworld.com/article/139974/2009/04/itunes_files.html

Where are my iTunes files located? - http://support.apple.com/kb/ht1391

iTunes 9 [and later]: Understanding iTunes Media Organization - http://support.apple.com/kb/ht3847 - plus supplemental information about organizing to new structure https://discussions.apple.com/thread/6477809?answerId=26404702022#26404702022

Image of folder structure and explanation of different iTunes versions (turingtest2 post) - https://discussions.apple.com/docs/DOC-7392 and making an iTunes library portable.

In your case unless you want things to get very messy very quickly the best thing is to choose which library you want as your starting copy, then add any media files you think are not in that library from the media folder used by the other backup. If you want hugely messy you add all media files just to be safe and then spend a week or two sorting out the duplicates one by one. If you want immensely, hugely messy you do the former and import the other library file into the first one and sort out all the duplicate playlists created in doing so as well as all the duplicate media files. I mean for me I know yesterday's backup is last week's backup plus new media plus changes I have made, so I don't really need last week's backup unless yesterday's backup drive has fried. I only really need one or the other.