> Can I use Mathjax to convert a TeX equation to a .png image?
No. MathJax does not produce images, it produces either: (1) HTML-with-CSS using math fonts to lay out the mathematics as positioned text on the page, (2) an SVG graphics version of the math, or (3) a MathML version of the math. It would be possible to use the SVG version and convert that to PNG, but we don't have anything packaged up do do that. There is a phantom.js implementation of converting a TeX expression into an SVG one as a command-line program. It was also converted to a web service called svgtex (
https://github.com/agrbin/svgtex), and been modified to produce both SVG and MathML for use with MediaWiki as a product called Mathoid (
https://github.com/gwicke/mathoid). You might be able to take one of these and add the SVG to PNG conversion to get what you want.
Davide