There are two bookmarklets here called "rendering off" and "rendering on" that turn off and on the MathJax rendering. When rendering is slow, turn it off for editing and back on to view.
The SE input box processes what is essentially
MarkDown is not yet standardized, and there are many different implementations of it you can find on the internet, differing in quirky little ways. That said, those differences tend to be at edge cases that you are unlikely to hit in usual usage, and if it does hit you can always edit it after previewing it on the site to fix any problems.
As to software tools: there are no official offline tools. But in this answer I listed some software tools that support the
Markdown + MathJax combo which you can use for offline editing.