Car battery Light & sounds light crap & boils over

Ford Taurus 2002 SE 3.0L V6 - Vin:U
Mileage 128***
No check engine light. Only light on is the battery

1st Problem - Car Battery
When I drove the car to this restaurant to go deliver the food, the car was running fine even after pickup. But once I deliver the food by shutting my car off, the battery light would stay on and would stall in 2 seconds when it reached 1100 rpm and that was always the result. Waited a few hours the car started up the rpm rev high and the battery light went off but when we turn it off again the same thing happen over again were it would go to 1100 rpm and stall in 2 seconds. Also even when i try pressing on gas pedal while i turn it on it just quickly dies it wont rev up. Next Day I go there again while it was sitting for good amount hours. I turn it on the car kept reving up and got to 2500 rpm before i shut it off. Waited few seconds turn in on again and luckily it stayed on so i could get it home. Once i got it in the driveway i tried turn it on again but this time it would do the same thing as before rev to 1100 in 2 seconds and die even if i press on the accelerator it wont rev it up but die quick or even changing gears just the same result dies quick. Always had a issue with the Remote start were it will work and not work, put new battery in the remote and same results. Took the remote starter box out and still resulted same with the car battery.

Checked it with a meter the alternator was funky so i replaced it. Still the same results. Eventually after dad did something to the wires by the fuse box the car would turn on but still had to jump the car many times when ever we turn it off. Car revs up to 1500 rpms then shifting gears it goes to 1100 rpm. While shifting from reverse to drive the car would rev the rpm up quick for a second to drop back down to 1100 rpm. When putting in park it goes back to 1500 rpm.

Replaced the Battery and the battery light remains on. car still goes up to 1500 rpm then after letting it sit for a bit i was going do a test drive on it but the car is back to square 1 rev to 1100 rpm an 2 seconds later it rpm drops and stalls. Checked all the wires and fuses but there good everything is grounded right.

Second Problem - Black Smoke and other
I changed the head gaskets a month ago did everything right to it torque specs and gasket sealant. When taking out the front middle New spark plug there was allot of combustion on it (Today), while looking at the valve stems back when i changed the gaskets there was 1 black 1 grey. It sounds like it misfiring when the coil is good, the spark plugs were changed. Rods are aligned. There is no vacuum leak either. Also after i changed the head gaskets 4 hour driving in there was knocking noises but when i got it home and added more coolant in it the knocking went away and have not came back since. From the exhaust pipe it blows the black smoke out but it wasn’t doing it when i was getting it home that one day when i got lucky

3rd Problem - Coolant Boiling over
Reservoir cap was changed a year ago, While changing the head gaskets i put a new thermostat in it. Changed the idler pulley and tension pulley also. A year ago I put stop leak in it and then few months ago i been always having problems with the car reservoir boiling over were it spits out of under the cap of the reservoir. We put a pressure Gauge on it before the head gasket change and it kept building pressure.
The fans spin on the car.

At this point I have no clue what to do. I literally been trying everything and had other mechanics look at it but they dint know either.

Check the ground connection at the battery and chassis step 1 for me.

A huge amount of sometimes contradictory description with no mention of whether the check engine light is on, the codes it set or even the mileage. It isn’t clear whether it even runs or not right now.

Wanna clear some of this up for us?

The grounds are good an unsure what the chassis are

Mileage 128***
No check engine light. The only light on is the battery

Bad alternator or bad field signal to the alternator. Check the voltage when the engine is running, it should be 13.5 + volts. Check and see if you can connect to the ECU with a code reader/scanner. If the ECU has partially failed, the alternator may not be getting a charge signal. Check the signal to the alternator - the field connection - to see if there is any PWM there.

Problem 2,and 3 won’t matter if the car won’t run.

What do you mean when you say the rods are aligned?

I assume you changed both head gaskets. Did you check the heads for flatness? Did you have them milled, if so did you check to see if the intake manifold needs cutting.

Are the head bolts torque to yield? If so you are supposed to use new ones torqued to a certain value plus so many degrees.

The connection is good

Rocker arm are were there supposed to be.
Yes new head bolts and torqued correctly.
Yes also checked the heads level an wasnt warped.

When checked with a meter all the connection to alternator and battery were good. But still same results

The battery warning light is supposed to be on when the key is in the “on” position and the engine not running. That’s normal. Are you saying the battery warning light is on while the engine is still running ?

Correct battery light remains on even if it running.

Here’s a basic battery/alternator diy’er test. Volt meter required. Before the first start of the day battery should measure about 12.6 volts. Immediately after starting the engine, 13.5-15.5 volts. What do you measure?

I was measuring at 14.32 volts when it was on. While off i cant remember but it was 13 something in its recommend range.

The battery light is only supposed to turn on (when the engine is running) when the battery isn’t charging. If the battery measures 14 + volts it’s charging, so the problem is more likely the warning light circuitry rather than the alternator or battery. You might want to confirm this at a Ford dealership. On some vehicles the battery and brake light serve double duty, in the event one of the bulbs fails the other will turn on. Do all the other dash warning lights turn on when the engine is off, key is on? Especially take note of the brake warning light. Does it turn on when the engine is off, key is on?

when car is on the battery light is only on. is there a way to post pictures and videos in this chat?

When the engine is off, key is on, are all the dash warning lights that are supposed to be lit, actually lit? There’s nothing funky about the alternator connector, right? No burned pins or sockets?

Correct all the lights come on when the key is on but not at starting position.
Correct no burned pins or sockets no corrosion

Until you get this problem fixed, It doesn’t make any sense to worry about the charging or black smoke problems.

I’m guessing you have a cracked head.