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Do you mean you have coolant leaking inside the cab on the passenger side floor?
Unfortunately this means the heater core is leaking and needs to be replaced. Servicing the brakes would have caused no damage to this, it is just an unfortunate coincidence. to replace he heater core on your truck takes around 10hrs labor as the entire dash has to be removed.
Even if they did and AC inspection there isn't any way that the heater core could be damaged. The only thing is if they had the heater hoses off and lost the oring seals, then coolant could possibly spray into the heater case.
Yes, to access the heater case to remove it and change the heater core the dash assembly has to be removed.
The dash comes out as one piece.
Yes, that is correct.