1, simply put, NO!. FUU is a utility to update firmware eg.. OTA updates (if you are unable to update normally)
To flash any rom you need....unlocked bootloader, custom recovery (to gain root) and maybe s-off depending on which rom you choose to flash and depending on which hboot
you have (all is explained in these threads)
2, not if the data is stored on /sdcard and you only factory reset which wipes data, dalvik and cache (not internal memory eg../sdcard)
3, if you are rooted, install xposed framework. then install 30 steps volume module or search xda for sound mods compatible with your rom.
hope this helps ( all the info you need is on here, so just search the threads)
Htc One Mini | Candy Rom| TWRP 184.108.40.206 | HBoot 2.22 | S-OFF | SuperCID | Slim Gapps (min)