Where can I find a collection of past exams w/ answers on various subjects?
MIT's Open Courseware project has a lot of material of this sort.  Here is a link to the Course Finder, with courses organized by topic.  The depth of the offering will vary from course to course. Some have only syllabi, others have complete video lectures, homework assignments, exams, solutions, etc.  The coverage is quite broad and includes courses in all of the specific classes you have listed.