You shouldn't be able to write to /usr or /home or / as a regular user, only as root, so that's normal. When it comes to writing to FAT32 partitions, you can set the user id (uid) group id (gid) and permission masks (dmask, fmask) for directories and files on FAT filesystems when mounting them. So:
mount /dev/whatever /mnt/whatever -o uid=yourusername,gid=yourgroup
will give you the ownership of the files on a FAT filesystem. By default ownership is given to whoever mounts the filesystem (in your case root). You might also want to experiment with fmask and dmask options (try dmask=777,fmask=666 and if that doesn't work try dmask=000,fmask=111. I don't remember which way is right). Take a look at mount command's manpage under subtitle: "Mount options for fat" for more information.