Car accident repair & insurance questions - Is it TOTALLED?

[VQTRVA]

My Mother's M.3MR was in an accident back in September.
Background:
Oncoming traffic stopped to let her turn left but oncoming guy in right turn only lane decided to go straight across the lane's solid white lines & ran into her front right side.

Police report classified my Mother's action as "No Improper Action".

However, report comments did state: "other driver failed to obey marked lanes & proceeded straight in right turn only lane."
I can't tell from Police report if other guy was charged as his identifying column for his action in this incident is checked 'Other'.

Fast forward to today:
Tesla OEM repair shop estimate $23K in repair costs:

1. 13K in part
2. 9K in labor
3. 1k in towing

A lot of it suspension related work then body work.
Though the most costly part listed for repair is the something called the 'Gear Assembly' which worries me because it sounds like motor related.


Question:

1. I think I had read >30% of purchase price is the rule of thumb for classifying the car as totalled - true?
2. Who determines this classification?
   • How can I influence to have the car classified as totalled?
3. Can a repair shop begin repairs with who's authorization ?
   • I ask this because in email comunication with repair shop they said they got the parts in & have begun mechanical repairs. We've haven't authorized anything as far as I am concerned.

 

[Dan203]

Insurance usually decides if it's totaled or not. You might be able to influence them if it's right on the line.