The Thirteenth, Fourteenth, and Fifteenth Amendments are known as the Reconstruction amendments. They each had their function and were introduced and adopted within a few years after the Civil War.
The Thirteenth "freed the slaves" or outlawed slavery. The Fourteenth applied the Bill of Rights to all the states.
And the Fifteenth protected the right to vote against discrimination by the states due to race.
The "Times, Places, and Manner of elections" of Representatives is assigned to the states by the Constitution. In order to prevent the abuse of the rights of the newly freed slaves by the states, the Fourteenth Amendment included a punitive Section 2 referred to above. But this section became a "dead letter" - or moot, when the Fifteenth Amendment was passed. (I do not consider it moot, but that is another discussion}.
The Nineteenth Amendment rendered moot any reference to male citizens and the 26th Amendment did the same for the age limit of 21, both of which were detailed in Sec. 2 of the Fourteenth you brought up above, and I repeat - rendered moot. The matter of sex and voting rights denied to women by the states, was settled by the Nineteenth Amendment and was necessary because most states denied women the exercise of their right to vote.
Through the years, the Fourteenth Amendment has slowly but forcibly incorporated the application of its rights and privileges protections for ALL persons in the states, so that now there are no other rights and privileges that are denied women that are not affirmed and remedied, if necessary, by the present Constitution.
Edited for link:
http://www.findarticles.com/p/articles/mi_qa3805/is_200401/ai_n9379658That is a good discussion of Sec. 2 discussed above.
By all means, list them, if you know of any. Those you listed above have been historically remedied or rendered moot as I have discussed above.