Issues after schemas migration from mysql 4 to mysql 5.6

There are two things that came into focus once you posted the table structure

• InnoDB Table has Fulltext Index
• Your Character Set is Hebrew

Would you believe someone asked 7 years ago Does MySql full text search works reasonably with non-Latin languages (Hebrew, Arabic, Japanese…) ???

You should make sure you have that the Hebrew character set in your MySQL installation

mysql> select * from INFORMATION_SCHEMA.CHARACTER_SETS where CHARACTER_SET_NAME='Hebrew';
+--------------------+----------------------+-------------------+--------+
| CHARACTER_SET_NAME | DEFAULT_COLLATE_NAME | DESCRIPTION       | MAXLEN |
+--------------------+----------------------+-------------------+--------+
| hebrew             | hebrew_general_ci    | ISO 8859-8 Hebrew |      1 |
+--------------------+----------------------+-------------------+--------+
1 row in set (0.00 sec)

along with the necessary collations

mysql> select * from INFORMATION_SCHEMA.COLLATIONS where CHARACTER_SET_NAME='Hebrew';
+-------------------+--------------------+----+------------+-------------+---------+
| COLLATION_NAME    | CHARACTER_SET_NAME | ID | IS_DEFAULT | IS_COMPILED | SORTLEN |
+-------------------+--------------------+----+------------+-------------+---------+
| hebrew_general_ci | hebrew             | 16 | Yes        | Yes         |       1 |
| hebrew_bin        | hebrew             | 71 |            | Yes         |       1 |
+-------------------+--------------------+----+------------+-------------+---------+
2 rows in set (0.00 sec)

You could try creating a new table with the same structure and loading it.

METHOD #1

CREATE TABLE cars_ftr_a LIKE cars_ftr_a_new;
INSERT INTO cars_ftr_a_new SELECT * FROM cars_ftr_a;
RENAME TABLE cars_ftr_a TO cars_ftr_a_old,cars_ftr_a_new TO cars_ftr_a;

METHOD #2

ALTER TABLE cars_ftr_a ENGINE=InnoDB;

Then, go look into the error log and see if those same warnings reappear. If they do not, you are good to go. You should also look into tuning the InnoDB Fulltext Options.

UPDATE 2017-08-22 23:17 EDT

METHOD #3

Another thing you can try is to drop the Fulltext Index and create it again

ALTER TABLE cars_ftr_a DROP INDEX `fts_string`;
ALTER TABLE cars_ftr_a ADD FULLTEXT `fts_string` (`fts_string`);

Then, go check the logs to see if the same errors came back or not.

UPDATE 2017-08-23 11:04 EDT

METHOD #4

CREATE TABLE cars_ftr_a LIKE cars_ftr_a_tmp;
ALTER TABLE cars_ftr_a_tmp DROP INDEX `fts_string`; 
INSERT INTO cars_ftr_a_tmp SELECT * FROM cars_ftr_a;
RENAME TABLE cars_ftr_a TO cars_ftr_a_xxx,cars_ftr_a_tmp TO cars_ftr_a;
ALTER TABLE cars_ftr_a ADD FULLTEXT `fts_string` (`fts_string`);

Load new table without Fulltext Index. Then create Fulltext Index last.