Engine Overheating

I'm not sure where you would be getting these numbers from but 200 degrees is certainly not hot at all and actually below normal for most cars these days. Most electric cooling fans routinely don't turn on until about 225 degrees and are expected to run in that range. Most are not considered overheating until after 230 degrees.

Here are the specs for your particular fan system.

The PCM commands Low Speed Fans on under the following conditions:

* Engine coolant temperature exceeds approximately 106 °C (223 °F).
* When A/C is requested and the ambient temperature is more than 50 °C (122 °F).
* A/C refrigerant pressure exceeds 1,310 kPa (190 psi).
* After the vehicle is shut off if the engine coolant temperature at key-off is more than 140 °C (284 °F) and system voltage is more than 12 volts. The fans will stay on for approximately 3 minutes.

The PCM commands High Speed Fans on under the following conditions:

* Engine coolant temperature reaches 110 °C (230 °F).
* A/C refrigerant pressure exceeds 1,655 kPa (240 psi).
* When certain DTCs set

The water pump has nothing to do with pressure. It merely circulates.
If it's leaking that has to be repaired.

I already posted what the acceptable temperatures are. You are yet to determine if the gauge is accurate or not. A scan tool would give you access to the temp the computer is seeing.

You probably finally got all the air out of the system. If it shows up again after a period of time, that would point to a head gasket problem.

This sounds like it but to be sure we need to see where the coolant is going. This is what we need to do: when the engine is cold fill it up with water, then drive it until it gets warm then park it and observe under the car to see if you can see any leaks. also lift the hood to see if there is pressure in the system. this guide can help us:

https://www.2carpros.com/articles/car-is-leaking-coolant

Please run down this guide and report back.