Even if you flash an older firmware - once you connect it back to PC Companion you will be offered the latest upgrade available - For Alex, Rooting changes the kernal and if the kernal has been changed then it will be detected as modified software
I have tried this and is does fail or it will say could not verify - When updating manually via Flashtools they would untick a box but Root would still be lost - Now we use .ftf files that have been deodexed which allows root to remain
Yes you will but if your bootloader is unlocked then you will also need to relock it again you can use Flashtools for this by clicking on BLU and then follow the instructions to relock it
