Ajax/Jquery将数据推送到后端

Firstly I'm not sure if missing anything in my code other than the problems in my functions, but i digress. I'm new to jquery so I'm having difficulty setting up a registration page. In the form I'm trying to check for valid entries as well as checking the queries in the back-end using php. I set up 2 files one is an html file and the other is a php file. Using ajax the function was supposed to call the php file, but I cant seem to get it working and I'm wondering if I should just put all the code in the same file. Furthermore I'm unsure if the functions are even working at all because its not returning any status. I will post the code for the two files below. Any hints or tips would be greatly appreciated.Firstly I'm not sure if missing anything in my