The optimization process and recommendations:

1. Avoid Subqueries (query line: 8): We advise against using subqueries as they are not optimized well by the optimizer. Therefore, it's recommended to join a newly created temporary table that holds the data, which also includes the relevant search index.
2. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
3. Mixed Order By Directions Prevents Index Use (query line: 25): The database will not use a sorting index (if exists) in cases where the query mixes ASC (the default if not specified) and DESC order. To avoid filesort, you may consider using the same order type for all columns. Another option that will allow you to switch one direction to another is to create a new reversed "sort" column (max_sort - sort) and index it instead.

Optimal indexes for this query:

ALTER TABLE `Grades` ADD INDEX `grades_idx_min_mark` (`Min_Mark`);

The optimized query:

SELECT
        IF(Grade >= 8,
        MyStudents.Name,
        NULL),
        Grade,
        MyStudents.Marks 
    FROM
        (SELECT
            Students.Name,
            (SELECT
                Grade 
            FROM
                Grades 
            WHERE
                (
                    Grades.Min_Mark <= Grades.Marks
                ) 
                AND (
                    Grades.Marks <= Grades.Max_Mark
                )) AS Grade,
            Students.Marks 
        FROM
            Students) AS MyStudents 
        ORDER BY
            Grade DESC,
            MyStudents.Name