Does reducing the ride height cause any damage to the car?

Answer 1

As with almost all technical questions, the short answer is "It depends". To a certain point, the benefits of lowering outweigh the problems of a lower ride height. Too much lowering risks allowing the chassis of the car to bump into the ground, and lets the tires scrape against the inside of the fender, when hitting bumps, rises, or dips in the road.

On a vehicle using coil springs to maintain ride height, the easiest and usually safest method of lowering ride height is by simply replacing the springs of a vehicle with aftermarket lowering springs. In general, simply cutting existing springs results in serious problems with ride quality and handling, and is not recommended. Aftermarket coilover spring and strut assemblies (simply known as "coilovers") offer more customization options, but require finetuning by expert mechanics to get the most of them, as they tend to be fairly expensive.
No. The ride height is adjustable by adding or reducing the amount of air in the tires, ergo, any damage would occur in the tires, not the car.