Does slowing an automatic using the paddles instead of the brakes damage the gearbox?

Does it damage an auto gear box to use the paddle changers to slow down, rather than the brakes?

Do modern automatics offer any engine braking?

Over the years I have had several cars with an auto gearbox and have always been very happy with what seems to be appropriate engine braking when going downhill. A friend of mine has recently bought a...