2007 Acura engine light and emission light on code p1005

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sounds to me like a BAD CO2/Lambda Sensor Good Luck Mike L.

Start with the first mechanic who replaced the battery and have them check the charging system. (Alternator) They should have done this when changing a battery, to rule that out as a problem in the first place. Explain the problems you have been having, as a bad charging system can cause all sorts of electronics problems and have them check the engine codes and have them explain what they are.
You could also go back to the muffler shop and tell them their sensor replacement did not fix the problem and have them correct their work.
Diagnosing Alternator Problems EricTheCarGuy

P0400 Acura - Exhaust Gas Recirculation System Leak Detected

Hose, gasket, or egr has gone bad

P1005 is model specific, Dodge is a problem with the manifold tuning valve.
Code 158 and 157 are for a problem with the O2 sensor for bank two after the catalytic converter.
Code 128 is for a problem with the thermostat or the engine is not reaching normal temp.
The O2 sensor codes could be caused from the manifold valve or they could be caused by a faulty O2 sensor.
I would start with the coolant temp problem and work back.

SOUNDS TO ME LIKE A BAD CO2/LAMBDA SENSOR

P1004 describes a problem with actual performance of the short runner valve (SRV), something used in your active air intake system to improve performance above 4500 RPM at or near wide open throttle. Its job is to change the path air takes within the tuned passages of the intake manifold, switching from a longer port runner length that's beneficial at lower engine speeds to one better for maximum horsepower at high RPMs. While there is likely a technical service bulletin that applies to your 3.5 engine that states this is a software issue, it hasn't been my experience in real life. The problem is almost certainly with actual performance of the SRV actuator, which is equipped with a potentiometer to track its actual travel... or performance... when actuated. The potentiometer is what goes bad on these units, something serviced only with a new SRV actuator. You won't likely notice any running problems with the engine other than perhaps the loss of a little high-RPM performance, but the MIL will keep coming on until the problem is addressed. The SRV is one of two servo actuators bolted to the plastic upper intake plenum and is the once closer to the center of the engine. It's easily removed and replaced using common hand tools (10mm socket and short extension) and costs in the neighborhood of about $350 I believe. It would be covered under the basic 3/36 warranty but not by the extended federal emission warranty unfortunately. If you have any questions, don't hesitate to write back.

P1005
It is not serious, but it will effect gas mileage and performance. Click on the link below, it will give you info on the code and how to find the problem: Code 1005 PDF

I'll be glad to help.

err 3 is not an engine system fault code, a tyupical code looks like this P0420, this happens to be a evaporative emission system fault code.

being an 07 your car is covered for all emmissions related problems for 8yrs 80k miles under warranty. recommend taking to acura dealer,so as to incur no cost to you

it is a system ground circuit code