MVC Entity Framework Models and Relationships - asp.net-mvc

Question

im quite new to ASP.net and entity framework. I created a class but im just going to simplify it and take the example class from Microsoft. So here we go. These are all the example classes
public class Student
{
public int ID { get; set; }
public string LastName { get; set; }
public string FirstMidName { get; set; }
[DataType(DataType.Date)]
[DisplayFormat(DataFormatString = "{0:yyyy-MM-dd}", ApplyFormatInEditMode = true)]
public DateTime EnrollmentDate { get; set; }
public virtual ICollection<Enrollment> Enrollments { get; set; }
}
public class Instructor
{
public int ID { get; set; }
[Required]
[Display(Name = "Last Name")]
[StringLength(50)]
public string LastName { get; set; }
[Required]
[Column("FirstName")]
[Display(Name = "First Name")]
[StringLength(50)]
public string FirstMidName { get; set; }
[DataType(DataType.Date)]
[DisplayFormat(DataFormatString = "{0:yyyy-MM-dd}", ApplyFormatInEditMode = true)]
[Display(Name = "Hire Date")]
public DateTime HireDate { get; set; }
[Display(Name = "Full Name")]
public string FullName
{
get { return LastName + ", " + FirstMidName; }
}
public virtual ICollection<Course> Courses { get; set; }
public virtual OfficeAssignment OfficeAssignment { get; set; }
}
public class OfficeAssignment
{
[Key]
[ForeignKey("Instructor")]
public int InstructorID { get; set; }
[StringLength(50)]
[Display(Name = "Office Location")]
public string Location { get; set; }
public virtual Instructor Instructor { get; set; }
}
public class Course
{
[DatabaseGenerated(DatabaseGeneratedOption.None)]
[Display(Name = "Number")]
public int CourseID { get; set; }
[StringLength(50, MinimumLength = 3)]
public string Title { get; set; }
[Range(0, 5)]
public int Credits { get; set; }
public int DepartmentID { get; set; }
public virtual Department Department { get; set; }
public virtual ICollection<Enrollment> Enrollments { get; set; }
public virtual ICollection<Instructor> Instructors { get; set; }
}
Like i said this is just for a example im trying to get know it.
My First Question: Do you need something like DepartmentID When you already do public virtual Department Department?
Second question: When i have a Collection of data how do i add values or Ids to that collection in the controller i can find this anywhere.
Third Question: Can some one link me a complete MVC example application with proper relationships