My experience has been with truck mounted equipment. I would guess that the skid mounted equipment would work as well. I am more concerned about the experience of the pigging contractor. If they have good experience decoking Coker heaters, then they are probably OK. If they have not decoked a Coker heater, the likelihood of having problems with the pigging is much higher.
All the questions you asked are good ones to have with the pigging contractor and your maintenance department. Any new pigging contractor should be able to show good safety performance or you should not hire them. They should provide a written report after the decoking and should be able to track the pressure vs flow during pigging so that they can estimate the location of the pig in the heater coil. All the coke removed from the heater coil should be reviewed to determine if any metal shavings are present due to pigging too aggressively. All of these things should be discussed and agreed to before bringing a new pigging contractor into the site.