I have a lot of trouble with math and my son is getting these problems
in school. Please assist me with explanations and solutions (formulas
etc...)

Problem:  A  800 ? kg car is coasting on a highway at 45 mi/h. The
driver must stop swiftly, because the traffic is blocked by an
accident ahead of him.
 
(a) What is the total mechanical work done by the car against the
force of friction of the brakes until it stops?

(b) What is the force that the friction of the brakes, rubbing against
the disks of the wheels, exerts on the car if it takes a distance of
16 m for the car to stop?

 (c) What is the acceleration of the car while the brakes are applied? 

(d) How much time it takes for the car to stop? 

~to solve (a), use the definition of kinetic energy ; for (b), see the
law of conservation of mechanical energy; for (c), apply one of
Newton?s Laws of motion; for (d), apply the definition of acceleration
? use only SI units)

I object to the wording of part b of the question.  Brakes are rotary
devices and do not apply a force along the straight line over which he
car stops.   Force of the road on the wheels could be tackled in a
question like that.

a) convert mph to m/s and calc KE=(1/2).m.v^2
The work done is equal to this.

b) divide answer to (a) by 16  because work is force x  distance moved
in the same direction as the force
Parts b onward seem to assume you mean average force or acceleration -
as if these are constant values throught the braking process.

c) F=ma and you have F (force on car) from the answer to (b)
The mass (m) is stated in the question.

d) initial speed (in m/s) divided by answer to (c)

First off, it's strange that the instructions specify using only SI
units, but the speed of the car is given in miles per hour. But
whatever. 45 mph converts to 20.117 meters/s.

   The work done in stopping the car to a dead halt is just the
kinetic energy of the car in motion. The equation for kinetic energy
is:

E = mv^2/2

E = energy of the moving car
m = mass of the car
v = velocity (or more casually, speed) of the car

   Just plug the given values for these into the formula:

E = [800]*[20.117^2]/2 = 161,877.476 joules. This is the work done in
stopping the car.

   Newton's force law is simply:

F = ma

F = the force on the car
m = the car's mass
a = the acceleration of the car due to the imposed force. How do we
determine the acceleration? The time taken to brake the speed isn't
given. What can we do? Here's what: The work done in stopping the car
is the change in its energy between one speed and another. But a more
formal definition for work is

W = F*D

W = the work done
D = the distance over which the force is imposed

Algebraic manipulation gives

F = W/D

We know the total work (W = 161,877.476) and the value of D = 16 m. So
the value of F = [161,877.476]/16 = 10,117.342.

Just plug this into F = ma.

[10,117.342] = [800]*a

a = [10,117.342]/[800] = 12.647 meters/s^2 

   The time to stop then, in seconds, is just SQRT[12.647/s^2], or 3.556 seconds.

"I object to the wording of part b of the question.  Brakes are rotary
devices and do not apply a force along the straight line over which he
car stops."

   That's right. Of course, if the car is said *approximately* to
accelerate linearly, on a so-called straight length of road, then it's
*approximately* accurate to speak of the rotary brakes imposing a
linear force on the car. Ultimately, there is really a torque bwteen
the brakes and the rest of the car, and a torque between the car and
planet Earth. It's definitely a grade school testbook.

There is more discussion of this question at
http://hyperphysics.phy-astr.gsu.edu/hbase/exprob/motx2.html#c1
which can be good resource for similar question in the future
(not that we would not appreciate the business :-)

Comments did answer the question, and so perhaps only thing to add 
is that according to the above  0.8 x 9.8 m/s^2 = 7.8 m/s^2
is max deceleration one can get for a car. That does not mean that
calculations in comments are wrong, but rather that specifications
given are unrealistic (at least for a car on planet Earth).