Your questions do not make any sense. The first question should be: Find the Laurent series for the function f about a point c.
You have singularities at and , so you can do Laurent expansions in two different areas: and depending on where z is defined.
I have no idea what you're asking in the second question since you can find a Laurent series expansion for f on that is convergent. If these are real question from a course, post them exactly as they were given to you.