While it is totally possible to develop a math editor on top of MathJax, I highly recommend trying other solutions like MathLive (https://cortexjs.io/mathlive/demo), as they are, by far, best ground tested for browsers and mobile devices.
This project was kinda of a proof-of-concept using MathJax to render the mathematics elements and building an editor around it, it can work, but there are a lot of issues that must be handled, such as cursor and mouse events.
Maybe someday I'll come back to this project, but for now I will archive it.