A live axle, sometimes called a solid axle, is a type of beam axle suspension system that uses the driveshafts that transmit power to the wheels to connect the wheels laterally so that they move together as a unit.
A live axle consists of a central differential in a single housing that also contains the driveshafts that connect the differential to the driven wheels. The differential is connected to the engine via a swinging drive shaft and a universal joint. The complete assembly may typically be suspended with leaf springs, coil springs or air bags.
Trail braking refers to continuing to brake past the turn in point, and on into the corner.
Generally a driver will get all the braking done before turn in so that all the tires grip can be used to corner the car. Trail braking or having the foot trailing the brake pedal (coming off) as the car is turned will help the car pivot on turn in.
This is an advanced technique as it involves making the tire’s contact patch attempt to both continue slowing the car as well as turning into the corner. This makes it easier to over drive the corner, and lose time or positions in a race.