Do graduate admissions simply see the 'letter grades' for a course, or can they see the numeric grade and/or exam scores, too? Not a long question, but I'm curious if grad school admissions (I'm more concerned with master's programs instead of PhD programs, right now) take into account only the letter scores of courses taken ("A", "B", etc), or if they also see if you were very close to another score, i.e., an 89 in a class would be a B, but it's 1 point from an A. Or to them, "a B is a B, no matter how close you were to an A or a C"?

Also, do they see specific exam scores from courses, too? For example, in a class, on each test I got a better score, and ended up with a great score on the final (100%). Will this be taken into account, or will it never be seen? 

I realize this could be dependent upon specific admissions boards, but I would guess there's a "status quo" for how things are done.
The information we get about grades comes from the official transcript that you arrange for the registrar to send to us.  Whatever information is recorded there is what we see.  At the vast majority of US institutions I'm familiar with, this means letter grades only, converted to a numerical GPA using the four point scale. 

Based on what you write, perhaps "plus minus grading" does not exist at your institution (as it does at most, but not all, American institutions: apparently it was introduced at my university only just before I arrived, and there are occasional weird -- though minor -- holdovers from the former state of affairs).  If it does exist, then it goes on the transcript and is used to calculate GPA.  

More information about course grading could come from individual faculty members in the form of their recommendation letters.  It is fairly common for such letters to include additional information about performance, including performance on individual exams.  In general if you got a good grade in a course but feel that your actual performance in that course was outstanding in a way that the grade does not reflect, then the instructor for the course is a good candidate for a recommendation letter.  In your case you might want to consider getting a letter from the instructor of the course in which you did better and better, culminating in 100% on the final exam.  This is exactly the kind of academic trajectory that admissions committees want to see.