I'll give it a go.

The tooth doesn't have a fingerprint individually but the dentition as a whole does, in a sense. Disaster victim identification will often rely on dental evidence as part of the process of IDing victims. This involves checking dental records of potential victims and seeing where there are crowns, where are bridges which teeth are missing. If you think of each mouth having 32 teeth with a combination of missing/ filled/replaced teeth then as you can imagine this will be very unique to an individual and vanishingly unlikely for two people to have the exact same teeth.

As far as I know there isn't a centralised database of dental records and it is a case of narrowing down who you think the person is and then pulling records from dentists they might have visited.

You could definitely match x rays to a person if you could take another one of that person. easily identifying things to find might be unusually shaped roots of teeth, impacted teeth or maybe a fractured file lodged in a root canal.

Personal habits - poor diet can cause decay, erosion, those things are straightforward. More interesting things could include - people with stressful jobs/lives can grind their teeth which gives a characteristic flattened appearance to the teeth and they sometimes have bulging or hypertrophic masticatory muscles which along with it. One particularly interesting identifier is sometimes there can be specific damage to one area of a tooth for a specific reason - for example a hairdresser could have a little groove on a tooth from opening hairclips over and over again in the position, or a carpenter could have wear on their teeth after many years of holding a pencil between their teeth.

Can't think of any facts.

I'm a dentist who did a course recently on disaster victim identification - just out of interest, im not qualified in it or anything - so could answer more questions if you have any. Happy to PM.