Welcome back, and I hope this is not your last question. We are always here for any automotive needs you have. LOL
As far as the water from the exhaust, that is perfectly normal and indicates to me the emissions system is doing what it should.
Next, when refilling the cooling system, you should have the heater on high so coolant can flow into the heater core.
Also, if the heat and AC are working and you are referring to the AC compressor turning on and off when the AC is on, that is exactly what it should do. It has to cycle or the internal pressures would get too high and rupture a hose or damage other components.
Now, the coolant leak has me concerned. Mostly, you have the upper radiator hose, heater hoses, and I believe the overflow reservoir to check. Here is what I suggest. Read through these links. They show how to pressure test a cooling system and repair leaks. It does require a tool to pressurize the system when the system is cold. However, most parts stores will lend or rent one.
https://www.2carpros.com/articles/radiator-pressure-test
https://www.2carpros.com/articles/car-is-leaking-coolant
The tough thing about a coolant leak is locating where it is located. Coolant can run in all different directions and come out in a place not even near the leak location. That is why I suggest pressure testing. Since it leaked when you lifted the vehicle, I have a feeling it puddled somewhere and started running when you put the vehicle on a tilt. Keep in mind, it is not uncommon for the radiator to leak around the plastic tanks. What happens is the crimps that hold everything together get loose and begin leaking. Also, it is not uncommon for a plastic tank to crack. I mention these things because I need you to look in those places too.
Let me know if you find it. Also, please feel free to ask any questions you have. I am anxious to hear what you find. I attached an exploded view of the radiator and hoses from it. Hopefully it will be helpful.
Take care,
Joe
Image (Click to make bigger)
Saturday, November 10th, 2018 AT 7:23 PM