The theme’s function file doesn’t “break” anything on the admin side. Sounds like you may have added some faulty code in by mistake.
Whatever issues you are having is due to an error in the custom code that you are adding to your file. If you are adding code to your functions file…or any php file, and there is an error in your code, then your entire site will break. This of course has nothing to do with the theme itself, you just have to figure what the error is in your code. So you may want to double check that you’re adding everything in correctly. Start fresh and add each code in separately so you can single out where your error is.
It’s highly recommended to use FTP and a html/css/php editor to edit your files just in case you make a mistake like this again, because if you do, you’ll be able to undo any errors. If you use the WP admin editor then you’ll be stuck on the error screen and it won’t allow you to go back (that’s just the way WordPress and PHP works)….so use FTP if you can.