Is there an API for reboot and various tasks?
I am wondering if is an API to do things like reboot() or perform other tasks - mainly reboot for me for now. If not, I would like to know if there is a way I can call reboot easily with $GET or $POST or simply accessing a URL without the complications of authentication.
No, not at this time.
If you must do something like that remotely, you could setup key-based SSH access and setup a passwordless key to run an automated command that way.
Or install package crond and schedule reboot etc.