Built house matches the design

Goal: the finished house matches the design as closely as possible - interior drawings as detailed as possible. Can the architect choose the furniture and work directly with the construction side, or is a supervision package needed? What if construction differs from the design or cannot be done? Does MM Home also take on the finishing work? What does the project management and construction supervision package look like? Is it supervision like 2 days/week plus days with important milestones (pouring concrete, waterproofing, foundation, floors...) or designer's supervision (making sure construction follows the drawings)? What is the cost?