Are these extra Index fields needed? 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&lt;&gt;0 AND total_rank&lt;&gt;0 


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!

Do I have to index final_point and total_rank to get faster select results just because they are in the where clause?
Provided you have an index on user_id (or a compound index with user_id as the first column) and a user does not have to many rows, you don't have to index final_point and total_rank.