I've designed a table as below for users who register a quiz:  

    CREATE TABLE `registered_quiz` (
     `rq_id` smallint(5) unsigned NOT NULL AUTO_INCREMENT,
     `user_id` smallint(5) unsigned NOT NULL,
     `iq_id` smallint(5) unsigned NOT NULL,
     `date` timestamp NOT NULL DEFAULT CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP,
     `is_registered` char(0) DEFAULT NULL,
     `delivered` char(0) DEFAULT NULL,
     `final_point` float NOT NULL DEFAULT '0',
     `total_rank` smallint(5) unsigned NOT NULL DEFAULT '0',
     PRIMARY KEY (`rq_id`),
     UNIQUE KEY `user_id_2` (`user_id`,`iq_id`),
     KEY `user_id` (`user_id`),
     KEY `iq_id` (`iq_id`),
     KEY `date` (`date`),
     CONSTRAINT `registered_quiz_ibfk_1` FOREIGN KEY (`iq_id`) REFERENCES `inja_quiz` (`iq_id`) ON DELETE CASCADE ON UPDATE CASCADE,
     CONSTRAINT `registered_quiz_ibfk_2` FOREIGN KEY (`user_id`) REFERENCES `karbar` (`user_id`) ON DELETE CASCADE ON UPDATE CASCADE
    ) ENGINE=InnoDB

And I have a query as below:   

    SELECT final_point,total_rank,rq_id FROM registered_quiz WHERE user_id=1111 AND final_point<>0 AND total_rank<>0 

 

First question:   
Do I need the part  KEY `user_id` (`user_id`) ? I was wondering if  UNIQUE KEY \`user_id_2\` (\`user_id\`,\`iq_id\`) would be enough!   

Second question:  
Do I have to index `final_point` and `total_rank` to get faster select results just because they are in the where clause?