Biddeford’s new restrictions on where some registered sex offenders can live will make most of the downtown area off limits and will primarily affect apartment buildings. The City Council unanimously approved an emergency measure Tuesday that makes it illegal for a registered sex offender who committed a felony and whose victim was under 14 to live within 750 feet of a playground, a private or public school, or other public property that mainly serves children. The residency restrictions were enacted in the wake of an ongoing controversy over decades-old sexual abuse allegations, some of them now under investigation. “It would be pretty much all of the downtown area,” Council President John McCurry said Tuesday, referring to the parts of the city that would be off limits.