以下查询操作使用SQL语句完成:查询共有多少学生 查询每个系有多少学生 查询选课门数在两门以上的同学的选课门数及其平均成绩 统计已有学生选课的课程的课程号，选课人数，最高成绩，最低成绩

针对这些SQL查询需求，我们需要假设相关的数据库表结构，例如：

1. 学生表（Students）包含字段：StudentID, StudentName
2. 系别表（Departments）包含字段：DepartmentID, DepartmentName
3. 课程表（Courses）包含字段：CourseID, CourseName
4. 选课记录表（Enrollments）包含字段：StudentID, CourseID, Grade

下面是对应的SQL语句示例：

1. 查询总学生数：

SELECT COUNT(*) 
FROM Students;

2. 查询每个系的学生数：

SELECT Departments.DepartmentName, COUNT(Students.StudentID) AS TotalStudents
FROM Departments
JOIN Students ON Departments.DepartmentID = Students.DepartmentID
GROUP BY Departments.DepartmentName;

3. 查询选课门数在两门以上同学的选课门数及其平均成绩：

WITH HighGraders AS (
    SELECT StudentID, COUNT(CourseID) as CourseCount, AVG(Grade) as AverageGrade
    FROM Enrollments
    GROUP BY StudentID
    HAVING COUNT(CourseID) > 2
)
SELECT CourseCount, AverageGrade
FROM HighGraders;

4. 统计已有学生选课的课程信息：

SELECT Courses.CourseID, COUNT(DISTINCT Enrollments.StudentID) as NumberOfStudents,
       MAX(Enrollments.Grade) as HighestScore, MIN(Enrollments.Grade) as LowestScore
FROM Courses
LEFT JOIN Enrollments ON Courses.CourseID = Enrollments.CourseID
GROUP BY Courses.CourseID;