1. I'm not sure if all railroads use the same principles, but I think the usual way is for the distributed braking car (some railroads call them 'repeater cars') is to take the signal from the brake hose in front and use it as a relay to send the same signal to the next cars. There are pipes and valves inside these air cars to direct the flow where needed:
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Train brakes are fairly rudimentary, in that they don't have variable pressure applications like you're used to in a car. They have only four positions - fully charged (fully released), partial application, full set-up, and emergency. So it's easy to send these simple types of applications through a relay.
The air cars have the added benefit of not only keeping up pressure, but also hastening brake release after an application by building up full pressure again more quickly.
2. "Do Not Hump" is in reference to special switching yards known as 'Hump Yards'. These switching yards start with a ramp or hill, so when a car is pushed into a track, it continues to roll by itself. It will be switched from track to track as it rolls, until it couples up with the cars in its intended final track, meaning the switch engine doesn't have to be connected the whole time it is being switched.
These cars can be slammed together fairly hard, creating a lot of shock, so certain cars are labeled "Do Not Hump" to ensure they aren't treated to this stress. A load of grain or coal doesn't care if it crashes into another car, but more delicate loads need to be switched slowly in more conventional methods. Automobile racks are usually labelled this way, for example.
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