How the hell do they pick up the train cars?
(It is probably something I can google, but you are a better story teller...)
Big, heavy machines.
Usually all the cars that are involved in a derailment get scrapped and shoved out of the way, the trucks are just held in place by a pin and when the cars tip over, usually the axles fall out of place.
The damaged cars and track are shoved out of the way, then my department comes in and we start with building a level grade, then start dropping in 40' sections of pre-built track and start rebuilding. We typically use trackhoes to unload track panels off of flat cars and put them into position, bolting them together.
Typically the goods that were loaded on the train are scrapped, the company is self insured so they just eat the damage to the freight.
The priority with a track like that is getting it back in service as soon as possible, we have had massive derailment with 30 plus cars on the ground and had the track back in service within 36 hours. If a track is not running trains, the company isn't making money.