With regards to designing for a mobile site, and particular to your question (03) - the number of mobile devices that's out there at the moment is astounding. What is equally astounding is the vast number of screen sizes that are now around, not only because of mobile phones, but also a large variety of tablets and small form factor PCs (Netbooks for example). To this end, I would not recommend designing to a fixed width, but rather take an approach where content can reflow on the page depending on the size of the screen.
Generally when building sites like this, a front-end developer would use a framework of some sort that utilises CSS media queries to adapt the site for various sizes.
There are of course several popular sizes, many of these frameworks will have a breakpoint at those sizes, and fluidly resize between the breakpoints.
Some good examples include:
How your design is put together by a developer is a bit of an art form, it requires some extra thought to translate a design to a mobile site with a responsive layout. (Without the designer needing to design all the possible layouts of course.)
Just my 2c