Car Hit the Tree

I hit the car to a tree while taking the right turn.
It hit the passenger side corner in front.
Car : Toyota Corolla 2001.

Car was at a very slow speed and impact was also not that major.

The collision is covered under insurance and its being repaired at auto body shop - approved by the insurance company.

I am kind of nervous - Not too sure if my car is in good hands.

1. How do we make sure that the autobody guys are doing what they are saying they are doing? I mean how do we make sure the repairs were taken care off properly.

2. Initially they said the work is to fix.
a. Head Light - Passenger side
b. Front Bumper.
c. Suspension
d. Little painting etc.

Now they are saying there is problem with
a. Engine Cradle
b. Steering Knuckle.

Though the impact was not major how do I make sure that it has affected Engine Crade and Steering Knuckle.

Will this change affect life of my car?
Do I expect Any problems due to these repairs.

3. As the repair cost goes up I am sure the Insurance premium will go up. How does the Insurance COmpany make sure that Auto Body guy is doing a good job at reasonable price.

I would appreciate your answer.

Thanks
Fatnani