777 is dangerous, especially with WordStress. If they are using mod_php without mod_ruid2, then this behaviour (can't write....) can appear.In most cases you will need to CHMOD the files and folders to 777
NO! In most cases you would NOT need to do this. Nowadays also Wordpress works mostly with 755 for dirs and 644 for files.In most cases you will need to CHMOD the files and folders to 777