It's probably brake dust or glazing.
Brakes sometimes will squeak from the dust in them. There's no good solution for it, although giving the brakes a good workout (more heavy braking) will help for a bit. A spirited drive along a curvy road should do the trick. You don't want to overheat the pads, just put a little wear on them.
You can also try pulling the pads off and lapping them. Place a piece of 180 grit sandpaper on a pane of glass, and rub the brake pads against this. Wear a good dust mask while you do this, you don't want to breathe brake dust. The idea is the same as the heavy braking. You want to break up the glazing on the surface of the pads that can form when the brakes are only used lightly.
I can understand why the Insight would get this problem, since we use regenerative braking most of the time and don't get on the binders that often or that hard.
There are various products out there that are supposed to stop the squeaking. They work for a short time at best.
Pull the front wheels and have a gander at the pads. If they're good, don't worry about the noise. Make sure that you check both the inner and outer pad on each brake.
Pulling the rear brakes is a little more work, since the drum has to come off. You'll need to block the front wheels and be on a level surface, since you have to disengage the parking brake to remove the brake drums.
While you're doing all this, bleed the brakes. It's not much work and is a good idea.
I don't see how it could be related to the IMA warning light. I'd chalk that up to coincidence, since the two systems are totally separate.
Fred