How to create Relationship between multiple databases?
Because all databases (schemas) on same server You can operate with data easy - just add schema name before table, like:

SELECT t1.* FROM database1.table1 t1 LEFT JOIN database2.table1 t2 ON t1.id = t2.id


same for compare and save result, like

INSERT INTO database2.table3
SELECT * FROM database1.table1 t1 WHERE NOT EXISTS (SELECT id FROM database2.table1 t2 WHERE t2.id = t1.id)


and etc

MySQL workbench can help You with compare schema

You can also use - mysqldbcompare