In my opinion, grad students (and job candidates) should have professional websites if (but only if) they have something to put there beyond research interests (and a barren CV). The websites should be professional, so little to no personal info and no pictures except perhaps one of yourself. They should include a statement of research interests, published or forthcoming papers, courses taught (with syllabi if possible), and CV link. Beyond that, you could include papers in progress or papers presented, but there are risks in doing that (such as those mentioned above). I tend to think the risks are not that significant (committee members don't have time to read a bunch of your papers and let's hope people aren't trolling websites to steal ideas and if they are they will be caught and banished). Personally, I think it looks nice if you've got a balance of published (or accepted) work with a few other papers in the works (or presented), and you include abstracts for each and links either to all or just the published and most well-developed papers. It's especially nice if it shows you have interests in several topics or fields and know what's going on in them.

I think the advice here would be similar to the advice I give our MA students applying to PhD students, who sometimes ask if they should use an undergrad teacher as a letter writer. If possible use these older references as a 4th or 5th letter, but if they will be a better 3rd letter than a current professor, there's no problem using it. I've never heard anyone complain about a job candidate's having 4-5 letters (rather than the 3 requested). Personally, I take it as a good sign, especially if they are all strong and at least one of the letters is from an outside expert. If you get a letter from an MA advisor, just make sure s/he can and will indicate that s/he's kept up with your work and finds your trajectory impressive.