~~no heat ~~~ random misfire~~~ two o2 sensors inactive~~~

When the compression is at it's peak at idle the cylinder pressure prevents the spark from occurring because of the high resistance caused across the plug gap. IT there is a problem in the carbon tracked leads and connections then the spark fails and the plugs misfire . So change the leads out for some good quality leads . Next check the injectors as they will also cause random misfire if they are dirty and squirting and not spraying

two things missing. Spark plugs itself, and o2 sensor.not mention

Check power steering fluid. "Whining" is too broad a term, sorry.

if the power steering fluid is leaking out of the pump itself then replace the pump add fluid and bleed all the air out of the system.the whining noise was the pump being low on fluid causing air to get into the system.if the leak is not the pump itself then you will have to find out if or which line power steering line is leaking,and replace the hose.the frothy mettalic look is the result of air in the power steering system.you may have to have it towed to a shop to have it repaired.if you changed just one plug why not all the plugs,this could be why it is running rough again,maybe even ignition wires especially if they are the original wires(10 years is good)

Did all these problems start at the same time, or did you let them accumulate?
I would start by changing the oxygen sensor.

whatever,change the O2 sensor,then recheck codes.

Frequent overheating is caused by low fluid level for coolant, coolant fan not working, or stuck closed thermostat.

The random misfire could be caused by a bad sensor like an O2 sensor, for example.

Wish you luck on this repair.

I own a 2004 V8
Have several hundred dollars in manuals

First -If it has a 3.9V8 it has to use 91 and most likely won't run well even on 93.
Second-the code you got is a PO 304,which is a bad COP Coil On Plug on cylinder #4. That is a common Ford failure. DO NOT replace ALL the Coils
Just replace #4 if that is the code. They are $59.00 and tax at auto part store.
I believe you need a 7mm socket and short 7mm wrench. Remove coil cover on top of valve cover,then coil. All same tools.
Third- FORGET the other codes. The LS will set all kinds of codes that will drive you crazy and go away,once you do the bad coil.
Fourth-one problem does not cause another
Fifth-The threshold bank code, is the result of the misfire and how the O2 Sensor sees things, as a result of incorrect fuel mixture (Misfire)
Make sure your O2 Sensors did not loosen up

Now the bad news

Expect-Coil Issues
- Bad Egr Valve
- Bad Trans Solenoid Trans Pack
Change the trans fluid -Mercon V
Flush the P/S Fluid-Mercon
Flush Brake Fluid
Flush Coolant-Yellow GO5
Cabin Filter- Remove round push pins on plastic wiper cover. Filter below on pass side
Gas Filter- Remove left front tire and loosen inner cover,next to door hinge

Use the OEM Spark Plugs
On a V8 -FR5AP-11E The were Motorcraft made by NGK
NGK-6569
Special Plugs.

Unless you have deep pockets-stay away from the dealer.
This is a very complex vehicle
Forget about gunning it. Baby it.

You need to have your power steering system flushed and new fluid put in it. Let's hope you haven't burnt up the power steering pump. Very common on the taurus. The fluid gets smokin hot because of the pump being so close to the exhaust manifold.

p1133 - o2 sensor, Insufficiant Switching, Bank 1 Sensor 1.
p0131 - o2 sensor circuit, low voltage, bank 1 sensor 1
p0171 - Lean condition, Bank 1
p0300 - Random Misfire

I would be looking at the front passenger side oxygen sensor for issues. It may be bad, it may not be plugged in, bad wiring at harness.

The random misfire may be symptomatic of the o2 sensor problem.