1990 CUTLASS CIERA 2.5L HAVING A HARD TIME STARTING.

MAF is probably not the problem - sounds like the engine is not getting the fuel it needs to start and either your injectors are fouled or the pressure regulator is stuck - that might cause the hot wires. The fuel pressure seems a bit low, but it should momentarily drop when trying to start the engine.

The internet is filled with all sorts of OBD1 Code 44 info to read

Bad Egr Valve --letting unmetered air in
Vacuum Leaks in the Exhaust Before the O2 Sensor
Bad Oxygen Sensor or corroded wiring
Vacuum leaks anywhere
Fuel Pressure too low
& more

You'd have to tee into the fuel filter to use a fuel pressure gauge,
if you got no shrader valve on the motor

You changed a fuel pressure regulator-- in the throttle body?

You won't see much with a scope on that system, if you scope
the O2 Sensor,their sort of slow compared to OBD2

Code 45 is for a rich O2 sensor. If you have already changed the sensor, the fuel mixture may actually be rich.
Possible causes include a leaking fuel injector, faulty fuel pressure regulator, or other problems.

The engine starts in "open loop" mode with factory default settings in the ECM. When it warms up, it goes to "closed loop" operation and relies on the O2 sensors to adjust timing, fuel, etc. Check for error codes (DTCs) using an OBDI code checker, or consider replacing the O2 sensors.

I would check for a short somewhere in the wire harness or check the bell for true on crank balancer make sure its not rubbing pickup

FUEL PUMP.
Have you checked the fuel flow and pressure?
If the fuel pump is over 160,000kms/100,000miles it's done.
Put in a complete assembly,if your mileage is close to above numbers you need a new pump anyway and it may (90% chance) will cure your rough running engine.The other 10 % is contaminated fuel and electrical, but as you have no codes I'll say FUEL PUMP.

If it has spark, the crank sensor is working. If the fuel pressure is 45psi, that's good.

Are the injectors pulsing controlled by the computer?

The Oxygen sensor is very suspect. it is easy to damage on install, even with the correct tool.

Put the old one back in and test the car...

sounds like an ignition module

i was just dealing with the same problem check out your fuel injectors , fuel pump, ingnition module with coil overs and possible fuel filter mine was the pump injectors and module its also a 93 cutlass ciera 3.3 fuel inj. hope this helps