I’m interested in something like the HomeStyle mortgage where you get money rolled into the mortgage to help cover renovations. However, I noticed the requirements say you have to put about 3% down. Is it possible to get one of these mortgages without any money down?

I’m not aware of any rehab loans that wouldn’t require a downpayment. Construction and rehab lending is risky business, and they like to have at least some level of protection.