If one of my questions says it was edited by another user, is there a way I can see what changes that user has made? Also, does that mean that question has become a CW?
There sure is - at the bottom of your question, it will state that the question has been edited and the time that it was edited.
Simply click on the time to see the edits made to the question.
To answer your other question, no - the question does not necessarily become CW. Details about CW questions can be found here.
Yes, you can click on the part that says "Edited N minutes ago" and it will show the edit history of your question.
It does not necessarily mean that it has become a community wiki, however after a certain number of edits (10 total, or by 6 different editors, I believe), it will automatically become CW.