To answer your first 2 questions:
iframe is supported across all the latest web browsers however i am not sure about mobile browsers. Opera mobile yes, dont now about iPhone.
the next major iteration of html is being led by WHATWG and the iFrame will be supported. It is also supported in xhtml
As far as different approaches, that very much depends on what you are going to be doing with the tabs. if each tab is going to have a lot of information on it or take a while to load then separate iFrames is probably best. Also, if you are going to reuse the code as independent pages else where then iFrames are also a good option.