Overheating?

When I turn the A/C on the air flow is super, strong on both sides.

Waited and waited on needle to move. But then only after I turned the A/C on it started to climb after a few minutes. I removed the cover on the heater core and both pipes are hot.

I cannot figure out how the cycle works. I think the lower one goes to the thermostat. Top one goes to engine.

Lower hose is super cold.

There is no cap on these radiators. So, I can't look inside. I'll remove the bottom hose and see.

Removed lower radiator hose and rusty water came down, but not much. Opened reservoir and more water came down but still not enough as expected from an open radiator. Rust is all over inside the reservoir and the hose. How do I remove the radiator? I guess this is where the issue is.

Removed radiator, not much water came out, I guess it wasn't taking due to all the rust inside, rusty water came out.I ordered another. The problem now is how am I going to clean all the hoses? Even the heater core am replacing since its easy. I disconnected the hoses on back of the engine and rusty water came out. No way to remove all these hoses as so many little ones divert from the big ones going to engine. I see rust inside the heater core hoses and the lower radiator hose, which goes to the thermostat.