Very high idling

I, feel sorry for you, after reading your problem, but don't worry you visit the Reliable-Store they will help you for sure.
2005 TOYOTA SEQUOIA SERVICE REPAIR MANUAL DOWNLOAD

Possibly a leaking injector or bad / stuck throttle position sensor.

battery not charging , means the charging system is not working , Doesn't mean the battery is bad . The charging system on your vehicle is computer controlled , If the BCM doesn't see the correct voltage , it will raise the idle RPM to over come any load on the system . Probably has DTC'S - diagnostic trouble codes stored in the BCM or PCM , These codes do not always turn on the money light ( check engine ) . Your best bet , take it to the Cadillac dealer , auto zone or any of those has no clue about this . Oh also it will shut down systems . http://www.esghotwire.com/0213_Pit.pdf
Battery symbo - Charging System Indicators

BATTERY NOT CHARGING - 7Charging System Indicators

BATTERY NOT CHARGING - 7
The IPC illuminates the BATTERY NOT CHARGING - 7 indicator in the DIC when the PCM detects a malfunction with the generator output. The IPC receives a class 2 message from the PCM requesting illumination.

I work for Cadillac , have for over thirty year's . Have seen people mess this stuff up big time . So do yourself an take to one of my fellow tech's.

Electrical Load Management
The power management function is designed to monitor the vehicle electrical load and determine when the battery is potentially in a high discharge condition. This is accomplished by using a high accuracy battery voltage reading as an indicator of battery discharge rate. The following six levels of load management will execute in the load management control algorithm when there is a high discharge condition:
The first action requests a vehicle idle speed increase to the powertrain control module (PCM) in order to raise alternator output.
The second action requests a greater vehicle idle speed increase to the PCM in order to raise alternator output.
The third action begins to shed vehicle loads in an attempt to remedy the heavy discharge condition.
The fourth action requests another vehicle idle speed increase to the PCM in order to raise further the alternator output.
The fifth action begins to shed further vehicle loads in an attempt to remedy the heavy discharge condition.
If the above five corrective actions fail, the sixth action of power management further sheds loads in a final attempt to remedy the high discharge condition.
Loads subject to reduction include the following:
• The A/C clutch
• The heated mirrors
• The heated seats
• The rear defog
• The HVAC blowers
The power mode master (PMM) calculates the battery temperature, voltage and charging rate at all times while the engine is running. The PMM calculates the battery temperature by factoring in:

Check out related help links to troubleshoot these problem:----Click the link below:---Idles Fine but RPM jumps in drive mode? http://technoanswers.blogspot.in/2012/07/idles-fine-but-rpm-jumps-in-drive-mode.html
---------Mitsubishi Lancer rpm needle bounces? http://technoanswers.blogspot.in/2012/02/mitsubishi-lancer-rpm-needle-bounces.html
--------How to adjust rpm on 2009 dodge charger SRT8?

http://schematicsdiagram.blogspot.com/2011/12/how-to-adjust-rpm-on-2009-dodge-charger.html
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Engine cuts out at 3000 RPM? http://schematicsdiagram.blogspot.com/2011/12/engine-cuts-out-at-3000-rpm.html

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Cold start problem and vehicle shudder around 2500 to 3500 rpms
http://repairhelpcenter.blogspot.com/2012/10/cold-start-problem-and-vehicle-shudder.html

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High rpm in neutral? Inconsistant high RPM in neutral? http://technoanswers.blogspot.in/2012/02/high-rpm-in-neutral-inconsistant-high.html

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Jetski Sputters and Low RPM? http://whatisbyme.blogspot.in/2012/07/jetski-sputters-and-low-rpm.html

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Fuel Injection Problem And RPM suddenly increases http://whatisbyme.blogspot.in/2012/07/fuel-injection-problem-and-rpm-suddenly.html

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2005 Toyota Highlander: Engine runs hard RPM below 3000? http://whatisbyme.blogspot.in/2012/05/2005-toyota-highlander-engine-runs-hard.html

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1987 Toyota Camry: RPM Drops going Up hills? http://whatisbyme.blogspot.in/2012/05/1987-toyota-camry-rpm-drops-going-up.html

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Cruise Control stops working, Excessive cranks to start the engine and RPM goes max 2500 http://whoisbyme.blogspot.in/2012/07/cruise-control-stops-workingexcessive.html

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1990 Toyota 4Runner: Engine cuts off when reaches 2000 RPM?

http://whatisbyme.blogspot.in/2012/05/1990-toyota-4runner-engine-cuts-off.html

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1999 Toyota Camry: Erratic stalling and high engine RPM at idle?

http://whatisbyme.blogspot.in/2012/05/1999-toyota-camry-erratic-stalling-and.html

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1995 Toyota LS: Misfire at idle or low RPM http://whatisbyme.blogspot.in/2012/04/1995-toyota-ls-misfire-at-idle-or-low.html

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Lexus RX: Tapping noise under Valve Cover At Low RPM? http://technoanswers.blogspot.in/2012/04/lexus-rx-tapping-noise-under-valve.html

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These will help.
Thanks.

Sounds like a dirty air filter is putting the mass airflow sensor out of range. The throttle position sensor is subject to physical wear, the age of your truck warrants replacing it. The coolant temp sensor controls the Idle Air Solenoid which determines idle speed ( cold, high idle, 1200 rpms open loop mode for the ECU) and (hot, low idle, 800 rpms, closed loop mode for the ECU) If the truck does not have a Mass airflow sensor, check the Manifold absolute pressure sensor (MAP). Perform an OBDII scan for stored fault history to avoid buying parts you don't need. Do the cheapest fixes first. Go ahead and change the fuel filter also. There is a lot of water in todays fuels

Sounds like a broken or torn vacum hose, pcv valve clogged, or bad Idle air control motor. Did you spray carb cleaner on vacum hoses or near the plastic intake., and did the motor rev up or down? Those codes represent a lean condition which means most like a vacum leak or clogged idle air motor. Sometimes the intake manifolds crack or the intake manifold gaskets crack. FInd that vacum leak or inpect iac motor

Sound like you could have a defective ISC (idle speed control) sensor.

idle air control motor or just a plain old vacuum leak

I had the exact same problem on my 04 GC. I put some Techron Concentrate Plus Fuel System Cleaner in from Wal-Mart and it seemed to fix the problems right away. Let me know.

check your anti freeze and watch your temp gauge.any check engine light on.