I am doing a Masters thesis. Can I use a quote to begin each chapter of my Master's thesis?
Epigraphs are generally fine unless otherwise proscribed by university rules or the style guide used in your field. (MLA has specific formatting guidelines for them, I'd imagine others do too)
But first ask yourself if they add something to your paper. For example, a quote from Borges on an section on recursion would go rather nicely, setting up the ideas/theme far faster than a stale introductory paragraph. A quote from a historical leader might establish a link between the past and a chapter on modern day politics or society. But an inspirational quote about hard work probably doesn't belong in methodologies chapter.
Well, I would say it depends on the context. If you are using the quote later for your work, or if it is connected somehow to your work, it is ok, otherwise the quotation would not have a purpose (for example in theory this can be a copyright law issue in some countries, e. g. Germany, whereby it is unlikely that someone will pursue it.).