I write them in a plain text file (in my case with gedit or Geany) and translate with pandoc:
pandoc --mathjax -s -o post.html post.md
That gives you a pretty good idea of what to expect on SE, provided you don't use Markdown features one of pandoc and SE does not support.
I should maybe note that I keep a record of the images I create (in files) since ...
Because the math can include things like \def, \label, \ref, etc., it turns out to be a more complex process to do incremental updates than you might think. I did a version of it here, but I don't think it works any more (hooking into the SE editor was fragile, and I think the code has changed since I wrote the userscript, and it no longer is able to hook ...
< is also the starting character of any HTML tag - which a subset of is allowed in markdown.
As such - it isn't escaped by the parser - and your browser thinks that everthing after < (until a > is reached) is a tag. So isn't shown on the page.
Solution? When posting math, use math formatting, as in the edited post.
I used to use notepages (demo, project). It was slightly annoying, because they use different open/close symbols for mathjax.
Then I started using stackedit (project), which works great, and integrates well with Google Docs/Drive and Dropbox. You can even install it as an App under google docs, which will create a stackedit document that will automatically ...