No, unlike auto insurance, if you own your home you are not legally required to carry insurance.
This will depend on who you’re lender is, but in the vast majority of cases, the lender will require that you carry insurance as part of the mortgage agreement.
There is no standard for what constitutes basic home insurance, so this will vary from company to company. Please inquire as to what the most basic insurance policy is before purchasing.
The deductible is the amount you are responsible for before your insurance kicks in. For example, if you have a $10,000 deductible, you would have to pay the first $10,000 for any claim before the insurance comes into play.
Most insurance policies cover you for instances of theft, though this needs to be confirmed with your provider before purchase.