As far as I know the "zu" you actually get when you type it is correct! The "sa" column of the hiragana table makes 's' into 'z' when you add a tenten (the " like mark). How you get "tsu" with a tenten is by typing in "du" because the "ta" column becomes "da" with a tenten.
Okay, that sounded a little messy in words, but did you get the meaning?
Anyway, about your grammer problem, I don't know of any books that are going to tell you the grammer of Japanese games, but maybe the open courseware on MIT is a start...?
Free Online MIT Course Materials | Foreign Languages and Literatures | MIT OpenCourseWare
Look for the courses about Japanese and you can get all of the course materials right online.