Hi and Welcome. My Name is ***** ***** I look forward to assisting you today with your question.
You shouldn't have changed root permission of 'everyone' because you are one of 'everyone'. The problem is your account is no longer able to access the core system and library files to boot the OS X. I hope you didn't lock down your entire system. Now we can try to create a brand new administrator account through Single User Mode, then change the permission of other accounts to what it was.
Follow the steps below to create a new User Account in Single User Mode.
• Turn off/Shut down your Mac.
• Turn it on and immediately hold down the Command(Apple) and S keys together for 10 seconds to boot into Single User Mode
• When you see the text prompt (Single User Mode), type in the following terminal commands to create a brand new Admininstrator account (hitting return after each line). Also, note down the spaces between the commands, like a space between mount and -, space between -uw and / etc
mount -uw /
shutdown -h now
(If it returns any errors, then you are entering the commands incorrectly. Make sure you enter it correctly)
When you enter last command and press return, the Mac will shutdown. So turn it on, you should be able to create a brand new Administrator account through the initial setup screen. You will not lose any files. Just login to new account,change the permission of 'everyone' back to read/write or at least change your account's permission to read and write. Then logout from Apple menu and login to your account.
Please let me know if that didn't work, so we can continue troubleshooting.