Is it ok to use the "body" part (of questions and answers) to render LaTeX equations for personal use?
In other words is it OK to use it as a LaTeX editor-compiler for non Stack related purposes?
As long as you don't submit the post, I don't see any harm in using the preview functionality of Stack Exchange to test your LaTeX code. But see Concerns about MathJax in proposed new SE editor – at the moment it's unclear whether that will continue to work. Otherwise, we have the Formatting Sandbox which can be used for this kind of stuff.
Note that the language we use here is MathJax, not the real LaTeX. I don't have enough experience to list the most important differences, but you might want to use an (online) LaTeX compiler instead. This question on TeX Meta lists two of them.
For personal use, you could use a template HTML file that accesses MathJax directly. The example template below uses the MathJax website. It also has a commented out portion in the header that you could use if you download MathJax to your computer.
Then simply view the edited template HTML file in almost any web browser.
If you just need to compile an equation, LaTeX2PNG is an option. As you could probably guess, it converts LaTeX to an image format.