Air trapped inside radiator after adding coolant

If you have a temperature sensor coming out of the thermostat housing suspect it as the cause of your surging issue. This doesn't even set a CEL light. You can change it same time as the thermostat replacement. Read the Honda groups on the Internet.

The low level of coolant won't cause engine surging, nor will air in the system. It is good to try to get it out though.

The rev surging might be an idle-control valve trying to do what it does. Have a good mechanic take a look.

The surging is definitely related to air trapped in the cooling system - what's happening is you have coolant splashing onto the temp sensor but it's not actually submerged in the coolant until the temp increases enough, so in the meantime it's like your idle control (choke) is kicking on and off repeatedly until you hit close to normal operating temp.

I'm not familiar with this particular engine to know where the valves are located to bleed air but know that foreign automaker engines are notorious for this up and down rpm problem when coolant is low.

If all else fails, you could try jacking up the front of the car to elevate the radiator and then run the engine for a good 20 minutes or so (make sure you hit full temp) with the radiator cap off to let all air work out of the system. If you see coolant level drop, add more coolant with the engine running until it's topped off and staying full.

I had a bad idle as well. Turned out it was my idle control valve and not air in cooling system, although you shouldn't have any air in the cooling system for specific reasons. Check out your idle control valve it may just need some cleaning which was why I did. I was getting close to the point where my car almost stalled. I drive a 2000 Honda Accord SE (6th gen) btw and no more idle problems :)

Just as a friendly tip check out these so called vacuum fillers:

Here's a hit on the product at Amazon UVIEW 550500 AirLift II Economy Cooling System Refiller

And here's a video of a fella demonstrating one.

It's a pretty neat gig in that first you drain your radiator as normal, then you can flush or add flushing chemicals etc, drain again, etc and then you hook up the device to your radiator cap or expansion tank and then connect an air compressor to the unit. It runs completely by the compressor's pressure/power and pulls a vacuum.

Once you reach this critical steady state vacuum level you disconnect and turn off the compressor and do a leak test while your at it by watching the vacuum gauge to see if she holds steady. If the vacuum holds then you have your premixed coolant handy in a clean bucket or other container and you stick one of the hoses into it. Some folks prefill the hose so that the small amount of air occupying the hose is avoided. Then you open a valve and the hose is now exposed to the vacuum set in the coolant system which basically causes the hose to suck in all the coolant until equilibrium or your run out of coolant so have enough handy. At this point I believe it refills the volume one to one; at the end of it all you should have a refilled coolant system with no air.