The WinMerge thing I don't understand it. I am pretty confident that all I have changed has been the Footer file. And I am ok with fixing that again.
If that's all you've changed, then it's best to just start afresh with a new copy and don't bother with migrating the changes you've done previously. Depending on how you want to customise the theme's footer, you can probably find the how-to in this forum already.
So whats the next step, creating a child theme? and how ?
Yes. See http://docs.graphene-theme.com/Customisation_using_a_child_theme
And is FileZilla connected to my website?? So if I want to change something on my site, do I make changes in Filezilla Or my website? or do I only use FileZilla if I want to change the Main Files like the .PHP Files ?
FileZilla is an FTP client. It connects to an FTP server. FTP denotes "File Transfer Protocol", so it gives you access to the files on your server so that you can modify, delete, create new file, etc.
When you change something via WP Admin, those changes are not made to the files, but to the site's database (except a few things that need file access, like uploading images or writing htaccess rules for permalink). If you can make changes via WP Admin, there's no need to make that change by editing or creating new files using the FTP client, except in some cases related to performance.