Now, I have solved the problem, just one email sent again.
I removed Fast and easy checkout (still don't know if this was the problem, but it changes the code too much so it's hard to customize the buying process with that in. So I would like to remove it anyway). Then I followed DrBytes advice " As far as identifying what code has been changed on your site, here's the most accurate process to follow: "
I downloaded WinMerge and compared which files had been changed and uploaded a new fresh install of those files. The problem was somewhere in admin. When all admin files were identical to the original files it all worked again. Just one email was sent.
Many of my customers prefer not to create an account, that's why I installed Fast and easy checkout from the beginning. But instead of uploading fast and easy checkout again, I uploaded Cowoa mod because cowoa doesn't mix with the files as much as Fast and easy checkout and it allows your customers not to create an account.