Yes, but not to prevent the car from moving. It’s to move the parking brake cable from time to time so that it doesn’t seize up when you actually need to use it.
No, but it won’t shorten the life either.
You can engage the parking brake either before or after the car is off. If you’re on a hill it’s a good idea to engage it before you remove your foot from the brake just to prevent the parking pawl from potentially binding a bit when you go to shift into drive.
Personally my habit is that taking my foot off the brake pedal is something that happens concurrently with physically exiting the car, which means my foot is still on the brake as I put it in park, engage the parking brake, turn the vehicle off, etc.
+1 to @shadowfax except for the following condition. In freezing weather, if you drive through slush, water or have some ice/snow melt in contact with the bottom of your car, then always park on a flat surface and do NOT set the parking brake. The water could freeze the brake in the on position and it will not release until the local temps go above freezing.
The parking brake is also a backup in case something goes wrong and the transmission doesn’t end up holding the car, such as in that recall with some cars not too long ago where the transmission could jump out of Park.
I always use my parking brake except in the slushy conditions described by keith.
Sometimes it is difficult to know which one is holding the car, the transmission or the parking brake. So I have told my wife that when she is on an incline, engage the parking brake, then while holding the regular brake, put the car in neutral and see if the parking brake is holding the car, if yes, then put in in Park and let go of the brakes.
I doubt it matters, that mechanism is designed to take a beating, but on my automatic truck I always engage the parking brake with the vehicle completely stopped and the transmission in neutral, before shifting into park; the idea of doing it in that order is it reduces the amount of force on the parking prawl, a gadget inside the transmission which prevents the car from rolling away. Cars weigh a lot, so it is possible-- but uncommon – to shear that prawl completely off. Not sure what happens to it when it gets sheared off. I suppose it just falls into the bottom of the transmission pan. Probably the most common way owners shear the parking prawl off is shifting into park while the vehicle is still moving.
How things have changed. The Civic started with train your biceps manual steering and it now has finger tip activated electronic parking brake switch. Check with your owner manual, but I would not be surprise if the parking brake is applied automatically when you shut off the car.
Parking brake so be applied before shifting to park to minimize the chances of the car resting on the park pawl. Along the same reasoning, the car should be shifted out of park before the parking brake is released. In case your wet shoe slips off the brake, the parking brake is still holding the car instead of slamming on the park pawl.
When you’re driving the car, you smoothly apply power to all the mechanical bits. When you let your car rest on the park pawl, you applies a shock load to those CV joints, differential gears, and the engine mounts.