Undercarriage damage usually refers to the wheels, suspension and axles. There can be a variety of damage to all of these parts...literally hundreds of possibilities from flat tires and damaged wheels to broken shocks, springs, steering mechanism and axles.
This answer depends on what damage the undercarriage has. If it is just minimal rust the it can be left with some anti rust protectant. If it is bent a body shop will need to attempt to straighten it out.
what should be included in a repair estimate
ALL damage to a car is repairable. The real question is can it be done cheaply enough to make it worth whyle and can it be done well enough to be as servicible as before the damage.
If parts of your undercarriage scrape on the speed bumps as you pass over them, yes, they could do damage to your vehicle.
You do not need the plastic cover on the undercarriage of the Beetle necessarily. It is designed to protect the undercarriage from road debris but it is not necessary to the function of the car.
It is not included.
Someone can get a car damage estimate from a number of companies such as Geico. Geico offers car damage estimates and appraisals, as well as car insurance.