In a master's thesis, should relevant theory be part of the literature survey? Does literature survey/review include relevant theory (from textbooks/old references) or should it only include recent publications? Should I place the theory as a separate chapter?
The age of theory really does not matter.  If there is a relevant contribution from the 17th century that still matters today, then it is includable.  It doesn't mean you should include it, but there is no reason at all to exclude it.  Because of the pressure of "publish or perish," many current articles are of poor quality.  Indeed, I just wrote to authors of an article because I felt they missed a very obvious explanation.

Conversely, there were fewer scholars the further you go back in time and they were often the pinnacle of the profession.  While there was less knowledge to work with, there tended to be greater rigor.  There are two important reasons to quote older works.  The first is when the older work implies a broader range of options than the profession has taken or unintentionally foreclosed a path of research.  The second is when an important element of prior theory is wrong.  A quotation from a prior author can illustrate how incorrect thinking developed.  For prior theory to be wrong, it has to make perfect sense as to how it is correct.  The error has to be subtle.

Your literature review should include prior theory.  The scope of that review should be deep enough and broad enough to cover the discussion of your research project.  You should be aware of controversies that could impact you, the timing of that discussion is irrelevant.  There is no virtue to an article written in 2017 and no reason to not quote older works, even including the ancient Greek mathematical writings.  There are good reasons to quote Euclid's Elements.

If it is in print, ever, it can be used.  Relevance is up to you and your advisor.  As to whether it should be in a separate chapter, we can't really help you.  You are writing a book.  It needs to make sense.  How can you best make sense.