First, Mike's answer is quite good. I will mostly expand on it and provide more details.
TeX
TeX is a language (a full programming language, actually) for typesetting documents. It originally output to a format called DVI which could then be converted to PostScript, PDF, etc.; more recent versions can output directly to PDF. You write a document with TeX instructions in it, and the TeX system will convert it into printable material.
TeX is used for a wide variety of documents, particularly in science and academia. Most people use it for things that other people would likely use Word for; however, the quality of its results are more on a par with InDesign or other major document layout packages, far superior what word processors generally yield. Designing specialized or ad-hoc document formats such as brochures, however, is probably easier with InDesign or QuarkXPress (although it is not impossible to do so in TeX/LaTeX).
TeX itself is quite low-level.
LaTeX
LaTeX is a macro package written in and for TeX that provides commands and defaults for writing larger documents at a higher level, taking care of things like sectioning, tables of contents, etc. In my experience, most TeX users do not write low-level TeX directly, but rather use LaTeX. LaTeX is not the only such package, though; ConTeXt is another macro package with a different design philosophy, but it sits at a similar level to LaTeX.
Usage
TeX and LaTeX are very widespread in some portions of academia, such as mathematics and computer science, due to its superb support for mathematical formulas. I have also heard that it is popular in some other disciplines as well, such as linguistics.
For the last question:
Go to Edit --> Preferences, and look under the Typesetting tab. Here, all the different tools for typesetting is listed. You can edit existing tools, adding more arguments, or you can create your own. It might be better to create a new, so you don't have to change back for other projects.
Best Answer
It is not very natural to go from a LaTeX document to an ereader (e.g. epub) file. The reason is that LaTeX documents (such as PDF) already specify a lot of information, i.e. they are typeset. Whereas ereaders handle a much more plain-text format in order to change the font size etc.
However, this same problem occurs when converting a LaTeX file to HTML. This problem has also largely been overcome. Which I why I would recommend you to compile your TeX file to a HTML file using e.g. HyperLaTeX. From here it should be easy to convert to a ereader format using one of the many ereader creators, e.g. Calibre or MobiPocket.