Hi, I am not a student yet, but I am considering entering one of Capella's PhD programs and have done some research on accreditation. Here is what I have that may answer your first two questions: The short answer is that a Capella degree is nationally recognized. If you would like, keep reading for more detailed information.
The Secretary of the U.S. Department of Education recognizes select accrediting agencies as reliable authorities regarding the quality of education or training offered by the institutions or programs they accredit.
To find a school’s accreditation go to the U.S Department of Education website at: http://ope.ed.gov/accreditation/Search.aspx

The database indicates that Capella University is accredited by North Central Association of Colleges and Schools, The Higher Education Commission since 01-01-1997.
Though the agency is in Minnesota, it has the authority to provide accreditation to a number of states, not just Minnesota, including Arizona, Arkansas, Colorado, Illinois, Indiana, Iowa and many more North Central states, as the organization's name implies.

The North Central Association of Colleges and Schools, The Higher Education Commission appears on appears on the U.S. Department of Education list of recognized regional and national institutional accrediting agencies.
The fact that the North Central Association of Colleges and Schools, The Higher Education Commission is a “National” accrediting agency as sanctioned by the U.S. Department of education means that degrees obtained from schools they provide accreditation are nationally recognized. You can get more detailed information about any school’s credentials by visiting the U.S. Department of Education website. I hope this helps. It surely helped me.

Ray