If you look at post number #4 in this it will show you have to find residues without computing the Laurent series

http://www.mathhelpforum.com/math-he...ms-152737.html

Yes your are correct in 1 that they are both removable singularities.

Your idea is sound for the 2nd part but you don't need all of the lower order poles for the first one

with have a pole of order 5.