Insurance for your business (such as when someone gets hurt or your computer gets stolen or your business burns to the ground) is usually required if you lease a building. I'd still recommend it if you work out of your home, but you'll need to document files and equipment much better and say you are a business so they cover you as such.
Now regarding contracts, that covers any fault as long as it's spelled out. In my over 17 years of owning my company, I've never had a lawsuit or any legal battles over work.
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