I would like to make a plugin that will monitor for (new file/folder, rename file/folder, delete file/folder) and sync the changes to WebDAV.
For the WebDAV part i could use cURL but for detecting file/folder creation/rename/delete in the current active project is there an API that would allow me this?

I don’t know about Sublime itself, but if all else fails you can always use this library for python:
github.com/gorakhargosh/watchdog

I’ve used it a couple of times in the past for quick hacks, it hasn’t failed me so far.