You can only define foreign keys for tables using the InnoDB file system.
The creation of a foreign key fails unless you have a primary key defined on the referenced table, and an index on the foreign key columns (in the source table). If you do not have these, the creation of the foreign key fails with Can't create table (which is not a meaningful error message).
AQT cannot display the Foreign Key information. This information appears not to be available through the MySQL ODBC driver.
The only way you can see the Foreign Key information is to view the table DDL (using the Generate DDL button or right-clicking a table and selecting Table DDL). This runs a MySQL function that retrieves the table definition.