2004 Honda Civic Heating and Cooling?

I have a question for anyone, including mechanics or mechanical engineers who are familiar with the heating and cooling system of a vehicle. So basically I will break down my experience into high speeds (freeway over 65mph) and low speeds (around 35-50mph).

At low speeds when I turn on my heat, nothing but air comes out and the needle slowly creeps up to read hot (H) in the panel. AC typically works but has been back and forth, sometimes it does and sometime it doesn't.

At high speeds when I turn on my heat, AC and heat typically works and the engine runs at normal temperature, until I get off of the freeway then it heats up and cools down again.

My fluids are full, thermostat is working, and there's no visible leak.
Timing belt and water pump are due for replacement.
Coolant hasn't been changed, car is at 140,000 miles.

My diagnosis is that since the water pump is due for a change, maybe its not working hard enough to pump the coolant through the system until enough centrifugal force is reached at high speeds from the timing belt.

Secondary diagnosis is that I have a clog somewhere in cooling system causing my vehicle to overheat because fluids are not reaching the radiator since I have never flushed the system.

Recently, a lot of steam (coolant) has been spitting out of the coolant overflow by the cap, indicating that the engine is running hot and the thermostat is activated via return hose to radiator, car runs hot regardless of an open thermostat.

Make sure you hear your fans coming on. Turn on your A/C and they should come on. If you have no leaks other possibilities are radiator cap or radiator restriction. One other possibility is head gasket ready to fail. Sometimes it's worth paying an hour shop diagnostic time to figure out a problem then when diagnosed you have the option of letting the shop perform the repair or you doing it yourself. Guessing can be frustrating and expensive while throwing parts at it.