Database Design

I have a users table, i also have one to many relationship, one user may belong to one course , one course can have many users when user is student.( i have roles and permissions from spatie)

I also have lecturer role : many to many relationship with course.

I have implemented my relations on models like:

class Course extends Model
{
 public function lecturers()
    {
				// A course can have many lecturers
        return $this->belongsToMany(User::class);
    }

 public function students()
    {																								//Get course's students
        return $this->hasMany(User::class);
    }

class User extends Model
{
  public function courses()
    {
//A lecturer can have many courses
        return $this->belongsToMany(Course::class);
    }

    public function course()
    {
																								//Get student's course
        return $this->belongsTo(User::class);
    }
}

I have two questions:

Is the above logic correct?

Also, i have a user's role , called admin where he is not assigned no any course, currently the course_id which is needed to make the relations ,is stored on users table, admin will never need that column, where should i store it? Leave it nullable is good approach?