mogrify is imagemagick and it is what resizes images same as GD2 resizes images. Images are resized to the dimensions you specify in admin upload options.
I can not say anything about suPHP but I know people run it and our software.
You do not say you get any errors and if paths where wrong you would. I would suspect here that whatever so called security measures you say where done is preventing imagemagick from actually working.
Like your host says imagemagick was reinstalled but did they actually verify it was functional.