Will the obstetrician notice injuries & old scars such as a vaginal tear?

Not if minor. I commonly perform labia minora procedures and women report back to me that their gynecologists are generally not aware ofnthenscars of it has not been brought to their attention. If however you have experienced major trauma such as a large tear or delayed healing, it may be obvious to any observer.
Not necessarily. Because this part of the body has a very good blood supply, injuries or tears can often heal with barely a noticeable scar. That is the reason labiaplasties and vaginoplasties are becoming so much more popular. The function and appearance can both be improved with surgery with virtually no scarring.
Possibly not. Since mucosa like the vaginal tissues heal so well, there may not be any visible scars. It depends on many factors such as whether the tear was properly repaired and the location of the tear. If it concerns you, ask your obstetrician about it.
It depends.... If you are asking will an obstetrician notice the scars from labiaplasty surgery, they can but rarely. Similarly if a traumatic tear is minor they might not notice it. It depends upon the degree of trauma or surgery that occurs beforehand. It is not a frequent issue with labiaplasty.