The battery is located in what would be the spare wheel well on a normal car. Honda claim that the battery will last the life of the car (taken to be 15 years or 150000 miles) - however, there have been reports of a large number of failures on the Civic hybrid (see https://www.insightcentral.net/forums...lure-rate.html
The Insight 2 has a smaller, simpler battery than the affected years of the Civic hybrid. It may be that the I2's batteries are more reliable but this remains to be proven. Time will tell.
We have still heard of comparatively few I2 IMA battery failures on this forum.
The IMA batteries are warrantied for 5-15 years and 90-150k miles, depending on where the car was bought and how old it is.
The part cost of a new battery is a little over £1,000 or US$1600 direct from Honda. I'd guess this will be about £1200 or $1900 including fitting.