Welcome,
The snake needs a hide at both ends of the tank and a warm end and cool end. The under tank heater should cover about a third of the floor space. You need a thermostat to control the heater and best bet for measuring the temps is to get a laser thermometer. Not sure what the temps should be for a king snake but am sure someone else can tell you
If the temps arent right then this could be a reason why it wont eat as it needs correct temperatures to digest its food, also snakes sometimes take a couple of weeks to settle into a new home.
The pink belly could be a burn or it could be about to shed (which could be another reason it isnt eating
) - can you show us some pictures?
Personally i wouldnt handle the snake at all until it is settled in and has eaten a couple of times for you.
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