Can I use my own material from my previous thesis (e.g., Master's) or article(s) in a current thesis (e.g, Doctorate)?

Yes—and you would cite yourself as if you were another author.  For example, if part of your doctoral thesis is carrying on work from your Master's thesis, introduce the concepts, paraphrase, and give the citation as you would for any other publication, and reference your Master's thesis in the References/Bibliography.  Direct quotations are also handled as if quoting another author, that is, give the citation and the page numbers from which the quoted material came.

If you wish to use articles you have already published in a journal, this usually isn't a problem, however, you need to have permission.  Check your agreement with the journal, search their website for information and, if necessary, contact them via phone. Include permissions as per the Copyright Permissions page.