Up until now, I’ve only been commenting on other peoples comments to nitpick. I think it is time to give you a comprehensive answer on my own:
You didn’t mention, what distribution you are using. Either way, you should use your distributions package manager to install zsh. Wherever that places the zsh binary is fine; you should not change that! If you want to know where the zsh binary is located, you can issue the command which zsh. That zsh should somehow be dangerous as a root shell because it is not POSIX compliant is nonsense. You can use whatever you like as a shell for root. If you don’t want to change the login shell for root, you can just start every shell from any shell by executing it’s binary (i.e. in bash type zsh, or the other way around). If you want to know what shells on your system are considered viable login shells by your system, you can issue the command cat /etc/shells; in your case it should list /usr/bin/zsh. If you want to change the login shell for a user, as that user run chsh -s … where … is the fully qualified path of a valid login shell; to be sure to not make typos or use an alternate path, you can combine that with which, and for example to use zsh use the command chsh -s $(which zsh). If you are the sole user of your system, I’d strongly recommend using seperate configurations for zsh for your normal user and root.
So now when I drop into a root shell I don’t get […]
Issuing su - or sudo -i or logging in as root in a full screen TTY (ctrl+alt+F*) will spawn a new shell (the login shell configured for root). If you are unsure, what shell you’re currently in, you can find that out, by issuing the command readlink /proc/$$/exe. If readlink is not available on your system, you can use ps -fp $$; be aware though, that that will show you the command the shell was started with, not necessarily the path of the shell executable.
If you want to write scripts you should always specify the shell it should be executed by with a shebang. For maximum portability/compatibility (do you like to distro hop? want to share it with a friend/the internet?) you should use env in the shebang. For you, if you want to script with zsh, that simply means always having #!/usr/bin/env zsh as the first line of scripts.