Friction
Kinetic friction is the force that stops a train when the brakes are applied
The answer depends on the mass of the train and the force applied by the brakes.
Assuming that the brakes are not "dragging" they start exerting force on the wheels when they are applied by the engineer.
It takes more effort to stop a car that does not have power brakes, although its rare to see a car without power brakes any longer. In either case, the literal answer to your question is yes it does increase the force applied to the brakes. Two feet are stronger than one. More force on the pedal translates to more force on the brake pads.
Gravity
An increase in applied force will cause the object to accelerate.
It depends on the decelerating force applied by the brakes.
An unbalanced force will cause an acceleration and a change in motion.
Liquids in hydraulic brakes help to stop an automobile by creating pressure and moving a set of pistons to generate force. This force is applied outward and causes friction that stops the automobile.
Forces cause motion or the change in motion.
The friction caused by the brakes causes the car to decelerate. This negative acceleration, in turn, causes a force to be applied to all those in the car. This is the lurch you feel.
That will happen if the force applied is less than the limiting value of the friction between the object and the surface that it is in contact with.