In order to add a domain that is to be used by someone else, and to prevent them from having access to your files, you should create a new user for them to use with the new domain. By doing that, they will have their own directory structure (similar to yours) that is accessible only by their user. You can, of course, still access/control stuff by just logging in as that user - the login and password is always available to you via the Control Panel (as you are the "master" account user.)
You can do this from the Control Panel-->Manage Domains-->Add a new domain/ sub-domain screen, where you can not only add the domain, but also create a new user to manage it at the same time. You can also add a new user at any time from the "manage users" section of the Control Panel, and then add the domain, assigning it to that user, but the first method does it all in "one step" .
There is no requirement that the new domain have a dedicated IP address just because your existing domain has one. As for the advantages / disadvantages of a static IP, it all depends on what you need the domain for. You will need a static IP address for VPN and SSL (and possibly other uses depending upon your software and purposes), but if you don't need those functions I see no need for a static IP address. Good Luck!