There are some StackExchange pages, as well as blogs, which have LaTeX integration, e.g. https://mathematica.stackexchange.com/. On these pages one can simply write math LaTeX code using the $ delimiters. Is there any EMail editor/plug-in for Ubuntu which translates LaTeX input to pictures, or keeps it as LaTeX, and parses it in a nice way?
If not, is anybody aware of a tool, in which one can input LaTeX code, and the output is an image? Drag&Drop is appreciated.
I do not know of any such integration, but I know the answer to your second question: Google Charts API.
Create an URL like the following:
http://chart.apis.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=AACCFF&chl=i\hbar\frac{\partial}{\partial t} \Psi(\mathbf{r},\,t) = \hat H \Psi(\mathbf{r},t)
clickable link to this URL...and there you have it, a PNG rendering of the LaTeX code you just wrote in it.
Email client
Since you didn't tell us what email-client you use. I assume you use the ubuntu standard one, mozilla thunderbird. Mozilla thunderbird has multiple addons you can use to insert latex into your email as a picture.
LaTex it! is one of the most promising addons.
https://addons.mozilla.org/en-US/thunderbird/addon/latex-it/
Off course you need to have a LaTeX environment installed on your computer.
Webmail
If you want a tool that you can also use for webmail. Then you could consider a LaTeX IDE such as Kile. Kile can output LaTeX as png.