If I shut down my pc while bitdefender is auto updating virus dabase will the files be damaged? in case of damage in virus database or the software will it tell you that files are damaged and need to reinstall?
No, it is safe to shut down your PC; it won't cause any issues with Bitdefender.
No. Shutting down during an update will not harm your PC. Bitdefender will usually detect a corrupted virus database the next time you start it, or repair it or offer to reinstall it, for example. So you don't have to worry about irreversible damage.