Does Rand al'Thor ever learn of his relationship with either of these characters?

Question

In Book 4 of the Wheel of Time, Rand al'Thor sees the history of his bloodline from the trip to Rhuidean, and then learns from the Aiel Wise Ones how he came to be born on the slopes of Dragonmount. At the time, however, the Wise Ones do not know that

his mother was Tigraine Mantear, Daughter-Heir of Andor before Morgase.

He does know, however, from the Wise Ones that she left an older child behind when she fled to the Aiel Wastes, so he at least knows he has a half-brother somewhere. Of course, knowing the first spoiler above, we as readers also know that this half-brother is actually

Galadedrid Damodred, later Lord Captain Commander of the Children of Light. He is also the nephew of Moraine Damodred.

Does Rand ever find out about this relationship, or for that matter does he ever learn of his mother's true identity before her adoption by the Aiel?

Answer 1

Yes, he does; he knows who his mother really was, and by extension, he must know how he's related to Galad.

It's made clear in Lord of Chaos that he knows who is mother is. I don't remember the exact moment when he pieces everything together, but presumably knowing his father was Aiel, and knowing the story of Tigraine from Elayne and others in Andor, eventually things "clicked".

This is most obvious in his discussion with Elenia (one of the nobles in Andor) about Andorian bloodlines. For a short period of time, when Elenia uses the word "cousin" to describe Tigraine and Morgase, Rand is afraid he's a blood relative of Elayne. He soon figures out that she's using "cousin" in a very broad sense, and is relieved:

Tigraine had not been related to Morgase. His mother had not been related to Elayne's mother. He was not related to...

Since he knows that Tigraine is his mother, and he knows that Tigraine is Galad's mother, it should be easy enough to figure out they are half-brothers. There are a few times in the series, IIRC, that he notes having a brother, but I don't know if he ever explicitly contemplates his identity.

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FWIW: Galad eventually learns about the relationship as well, from Gawyn, but that's much later in the story, at a point where Galad is willing to accept it.