So you do still have IMA lights on? You turned off the IMA battery? Why? The Insight does not have an alternator, the IMA system charges the 12 volt battery under the hood. Most of the time, the IMA starts the engine with the electric motor attached to the engine. You cannot operate a Honda hybrid without the IMA system. It is very rare for the IMA battery pack to be bad at your miles. You need to turn the IMA back on, make sure your 12 volt battery is charged and actually good (brand new batteries can be bad) You must load test that battery, not just measure how many volts it has when charged completely. You need to reset everything, drive around a lot, and see if the IMA light goes out. If it doesn't, you need to take it to a real Honda dealer as only they can read the IMA codes.
A more common issue with the IMA system is the cooling fan in back that cools the battery pack. Those go bad or the circuit that turns it on is bad. Or the vents to the outside are blocked.
Once at a real Honda dealer, make sure all the software updates are done. One of them specifically addressed IMA issues. There was a service bulletin on the software update and it should be done for free. There were others that affected how the CVT trans work, how the assist behaves on hills, and how the auto stop works. If you can beg them (or pay them) to install all updates, it is worth it.
Also, if, while driving around with the issues you are having and don't want the engine to auto stop at stop signs and signals, you can shift to S or turn off the ECO button. That is something you can do just to keep the A/C running. (re: Texas)