Hope that doesn't happen on a busy road.
no
Friction
A car slowing down when the brakes are applied.
yes, but only when the brakes are applied.
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.
When car brakes are applied, they create friction between the brake pads and the wheels. This friction slows down the wheels, reducing the car's speed.
When the brakes are applied, the car's kinetic energy is converted to heat by friction between the brake pad and the brake disk.
yes, that happened to me once..
Gravity
you need brake pads
Friction
Vibration when applying brakes is most likely warped rotors. Another cause could be loose caliper bolts.