1) Yes AND no. If php is running as CGI you are looking for trouble. Ask your ISP. ImageMagick is a good thing to have, too.
2) No. Unless the box that runs eZ is standing right by your side, you would never get root access anyway.
3) At least 12MB, yes. A solution that seemes to work, is creating "your own" php.ini and drop it in your eZ root folder. Worked for me.
4) Yes, but you only have to change permissions for the var-directory. 5) Probably, yeah. Setting up eZ (and understanding) is a lot of work! Don't give up.
Make sure your hosting service has compiled php with the GD libraries (the alternative to using ImageMagick). Most likely they won't have ImageMagick installed and probably won't let you install it. Check with them before you commit to EZpublish. As far as I know, if you don't have either one then you won't be able to use images in your site content at all! (I like EZpub a lot, but if you ask me, I think the disadvanatages of this requirement outweigh the advantages.)