A frost free fridge is nothing more than an ordinary fridge that has a way of automatically defrosting itself. Instead of the freon running through channels in the freezer compartment itself (as was the case on non-frost-free fridges), the evaporation of the freon occurs in a coil typically located at the back of the freezer compartment on a frost free fridge. That evaporator coil gets very cold (down to about -60 deg. F) and any humidity that gets into the fridge when you open the doors ends up in the form of frost on that evaporator coil. A frost free fridge will also have a defrost heater and a defrost termination switch (DTS) which melt the frost off the evaporator coil. The resulting melt water then flow down a tube to the bottom of the fridge where the melt water is re-evaporated into the air by the heat of the nearby compressor.

I expect what you saw was melt water from a defrost cycle that spilled onto the floor when you moved the fridge. I don't know why the water was a greenish colour.

Maybe the next time you move the fridge, wipe up the green liquid with a paper towel, and save the paper towel. If it dries up, then it's almost certainly water. The refrigerant in a fridge will evaporate almost instantaneously at atmospheric pressure and temperature, and the oil lubricant in that refrigerant is dark in colour and won't evaporate.

In your fridge's freezer compartment you should see a removable panel held in place with screws. To diagnose the problem with your fridge running continuously, you need to remove that panel and take a picture of the evaporator coil (which is what gets really cold) and the fan that's drawing air over the evaporator coil and blowing it into the freezer compartment. Take that picture to any appliance repair shop and they might be able to tell you what's wrong with the fridge that it's running continuously.

When you take that freezer panel out, you want to see frost forming uniformly all over the full length of the evaporator coil, no accumulated water or ice under the evaporator coil and the fan spinning to blow air into the freezer compartment. If that's what you see, then the problem is likely to be either the cold control or the defrost timer.

In fact, if you put your hand into the freezer compartment, you should feel a cold breeze from the fan. If you feel that breeze, then there's nothing wrong with the evaporator fan. However, the evaporator itself may be so frosted up that the air flowing over it doesn't get cooled enough to keep the fridge and freezer sufficiently cold.