Is a house that a minister lives in that is attached to a church called a mans?

No, a house that a minister lives in that is attached to a church is typically called a "parsonage" or "rectory," rather than a "manse." While "manse" is used in some regions, particularly in Scotland, it generally refers to a similar concept of a minister's residence. The terms may vary by denomination and location, but "parsonage" and "rectory" are more commonly used in many areas.