More MySQl2Derby notes:

Column Names

ResultSet rs = stmt.execute("SELECT COUNT(id) FROM tableName;");

if( rs.next() ){

    num = rs.getInt("COUNT(id)");

}

fails for Derby. You must use

rs.getInt(1); 

instead.

Getting last autoincrement value

stmt.execute("INSERT INTO tableName VALUES (LAST_INSERT_ID(), 'foo')");

There is no LAST_INSERT_ID() function, so in Derby you might try adding a new select statement and then using the results in later statements.

SELECT MAX(id) FROM tableName

and then set that value into a Java variable lastId to use in you INSERT statment.
Of course you want to turn autocommit off for executing multiple statement.