I am writing a workbook for highschool and college students to help
them get along better with instuctors and other students. Because I am
a Harry Potter fan and to help the book get recognition in the
marketplace: I am discussing in my book, how the Harry Potter
characters interact in the Harry Potter books.
Amazon lists more than a dozen books with titles like 'the unofficial
guide to magic spells in Harry Potter' or 'the science of Harry
Potter' etc.
So far, searching the internet I have found advice to fan-fiction
writers, but nothing that applies to my case. I surmise (I am
guessing) that I mustn't include a lot of quotes from Rowling's books,
I can talk ABOUT her characters, but I musn't put new words into their
mouths or make them characters/actors in MY book. But I want to know
exactly what the rules are that define and govern copyright
infringement when writing ABOUT someone else's books and movies. And
what about the Title of my book, am allowed to call it "Harry Potter,
Anger Management and You"?

Copyright law recognizes situations of "Fair Use"--that is, cases
where it's OK for someone to use bits of a copyrighted work in another
work. However, the laws are written in such a way that every situation
has to be looked at on its own merits; there is no hard and fast rule
that says "If you use X amount of a copyrighted work, you're OK, but
if you use X+1 amount, you're in trouble."

Claims of fair use are judged (when they are judged) on the basis of
several factors--the kind of work that's appropriating the copyrighted
material; the nature of the work being appropriated; the amount of the
copyrighted work being used; the potential effect of the use on the
original's marketability--and while you (or a lawyer) can make good
guesses as to your use with those factors as a guide, the reality is
that you don't know if your use is a fair use until you're caught,
sued, go to court, argue that yours is fair use, and the court decides
that you're right.

That said, use of copyrighted works for reasons of educational
purposes, criticism, or comment is generally held as a factor that'd
encourage a decision of Fair Use, assuming all the other factors in
the case are equal.

Also, note that although titles are not subject to copyright, they are
sometimes subject to trademark. The fact that there are other books
with titles including "Harry Potter" indicates that you'd probably be
OK with the title "Harry Potter, Anger Management, and You" provided
that you make it very clear that your book has nothing to do with the
original HP series of books or movies. (You might run language to that
effect on the cover. You definitely want to use very different logos
and type design, etc.)

Maybe someone out there works for a publishing house and can comment
on their policy for accepting manuscripts that talk about other
people's books, etc.

OK. I work for a publishing company and can at least comment on a few things.

(1) Basically, tr1234-ga's comments are right on target.

(2) As far as a publishing company's policies on accepting manuscripts
that refer to third-party works goes, you gotta realize that this
"policy" (such as it is) will vary from publisher to publisher--and
even from project to project.

(3) Writing a book proposal and pitching your manuscript is itself so
much hard work that it may not be worth it to agonize a great deal
about this aspect of your book at this point. Yes, you'll need to deal
with this eventually, but the first thing would be to get a publisher
(or agent) interested in your book; once you've gotten some interest,
you can work with those interested parties together to deal with
whatever rights issues might arise. So, for the moment, maybe all you
need to do in your manuscript submission is make absolutely clear in
your cover letter that (1) your book is not an official, authorized
tie-in to Harry Potter and (2) you believe your appropriation of
third-party material qualifies as Fair Use.  (The publishers and
agents you submit to can always have their own lawyers vet your book
to see if they agree with your belief in Fair Use, but bringing it up
first shows you have a bit of understanding of the situation.)

(4) If it is determined that third-party permissions are required,
it's often the responsibility of the author to obtain them. The
publisher may assist somewhat, and in extraordinary circumstances may
offer some amount of money to pay for incurred permissions fees. But
if it's decided that Fair Use doesn't apply in your case (or if the
publisher would prefer having official permission rather than rely on
the vagueness of Fair Use,) then it might well be you--the
author--who's going to be responsible for getting those permissions.

(5) All that said, realize that a typical book publishing contract
includes language where the author makes certain warranties--that
he/she is actually the author of the book; that the book is not
libelous; and so on. Typically, one of these warranties is that the
author has obtained all necessary third-party permissions for material
in the book. So when you get to the point of signing a contract, be
sure the warranties you're making match what you're comfortable
making.

(6) Just as there a lot of books with helpful information on how to
get your book published, there's no small number of books about Fair
Use and copyright issues (such as FAIR USE, FREE USE, AND USE BY
PERMISSION by Lee Wison). It's probably worth doing a bit of research
on your own to make sure that you're comfortable with writing what
you're writing--and that you know what you're asking your publisher to
do if you're relying on Fair Use.

Good luck with your project!