MySQL 8.0

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.
CREATE TABLE Data
(
    `order` varchar(10) NOT NULL,
    sn varchar(10) NOT NULL,
    ag varchar(10) NOT NULL,
    af varchar(10) NOT NULL
)
INSERT INTO Data 
(`order`, sn, ag, af) 
    VALUES
('a','0001','123','0'),
('a','0001','124','0'),
('a','0001','125','0'),
('a','0001','126','0'),
('a','0003','123','1'),
('a','0003','123','2'),
('a','0003','124','0'),
('a','0003','125','0'),
('a','0003','126','0'),
('b','0005','123','0'),
('b','0005','124','0'),
('b','0006','123','0'),
('b','0006','124','1'),
('b','0006','124','2'),
('b','0006','125','0')

Records: 15  Duplicates: 0  Warnings: 0


SELECT `order`,
        SUM(bb) AS bb,
        SUM(ff) AS ff
FROM 
(
	SELECT `order`, sn,
 	        CASE WHEN rule1>0 THEN 1 ELSE 0 END AS bb,
 	        CASE WHEN rule2>=1 AND rule3=0 THEN 1 ELSE 0 END AS ff
	FROM 
	(
		SELECT `order`, sn,
		        SUM(CASE WHEN af<>'0' THEN 1 ELSE 0 END) AS rule1,
		        SUM(CASE WHEN ag='126' AND af='0' THEN 1 ELSE 0 END) AS rule2,
		        SUM(CASE WHEN ag IN('123','124','125') AND af<>'0' THEN 1 ELSE 0 END) AS rule3
		FROM Data
		GROUP BY `order`, sn
	) AS A
) AS B
GROUP BY `order`
ORDER BY `order`


order
bb
ff


a
1
1

b
1
0