You are tasked with designing a conceptual database schema for the King Fahad General Hospital. The system needs to store information about Patients, Doctors, Departments, and Medicines. Explain in detail the fundamental database concepts you would consider during the design phase. Discuss the importance of entities, attributes, and relationships. Additionally, outline your proposed database architecture's potential challenges and benefits, considering factors such as scalability and data integrity.

Design a database starting from the conceptual design to the implementation of database schemas.