Cersei's children are
all dead, so she became the ruler.
I am wondering what Cersei thinks about the heir and the family's legacy her father talked about.
Given that she regularly has sex with her brother these days, can she give birth to her brother's child once again?
Yes.
In season seven,
she becomes pregnant with Jaime's child. Presumably this will be an important part of her motivations duration the story's climax, particular as Jaime himself has now abandoned her to fight the Night King with Jon.
When Tyrion goes to see Cersei to bargain for her help her actions indicate to him that she is pregnant. Tyrion then heavily suspects this and asks her outright and we get no answer. However, note the bottom line from the quote below which heavily implies she is in fact pregnant. But also note "Tyrion sees what he sees, and knows what it means." which is also implying that Cersei is doing this on purpose so Tyrion will think she is pregnant, i.e. is she manipulating him?
TYRION: She knows herself. She chose an advisor who would check her worst impulses, instead of feeding them. That’s the difference between you.
CERSEI: I don’t care about checking my worst impulses. I don’t care about making the world a better place. Hang the world.
Cersei folds her hands across her stomach.
CERSEI: That thing you dragged here, I know what it is and I know what it means. And when it came at me, I didn’t think about the world. Not at all. As soon as it opened its mouth, the world disappeared for me, right down its black throat.
Tyrion notices the barely perceptible movement of Cersei’s bottom hand over her belly.
CERSEI: All I could think about was keeping those gnashing teeth away from those who mean the most to me. Away from my family.
Tyrion sees what he sees, and knows what it means. He can hardly believe it, but he knows it to be true.
CERSEI: Maybe Euron Greyjoy had the right idea: get on a boat, take those who matter--
TYRION: You’re pregnant.
She stays silent for too long, long enough to tell him that he’s right.
And once she knows he knows, she can think of nothing else to say.
Game of Thrones, Season 7 Episode 7, "The Dragon and the Wolf"
She then makes some sort of a scene with telling Jon and Dany in front of Tyrion that she will march her armies north to help in the Great War.
And then Cersei enters behind him, with Jaime, Qyburn, the Mountain and the Queensguard in tow. Varys reenters as well.
CERSEI: My armies will not stand down. I will not pull them back to the capital. (beat) I will march them north, to fight alongside you in the Great War. The darkness is coming for us all. We will face it together.
This is the last thing anyone expected to hear. Dany and Jon both look at Tyrion.
Tyrion meets their gaze with a subtle expression: Tyrion Lannister, motherfuckers.
Game of Thrones, Season 7 Episode 7, "The Dragon and the Wolf"
However, as we find out later on Cersei does not intend to send her armies north at all and it is all a ploy. It is very possible that the pregnancy is faked to make sure Tyrion believes her and to also try and make him look foolish to Dany. We know Cersei hates Tyrion and that Tyrion's plans have all pretty much failed for Dany and so he is skating on thin ice. It is likely Cersei is trying to make him look worse.
CERSEI: What are you doing?
JAIME: Preparing the expedition north.
CERSEI: The expedition north. (beat) I always knew you were the stupidest Lannister.
Jaime opens his mouth but quickly closes it. Painful experience has taught him not to interrupt Cersei when she’s about to begin a rant.
CERSEI: The Starks and Targaryens have united against us-- and you want to fight alongside them? Are you a traitor or an idiot?
JAIME: You pledged our forces [to fight our common]--
CERSEI: (speaking over him) I will say whatever I need to say to insure the survival of our House. You expect me to trust the man who murdered our father? You expect me to command our troops to fight beside foreign scum? To fight for the Dragon Queen?
JAIME: You saw it with your own eyes. You saw a dead man trying to kill us.
CERSEI: And I saw it burn. If dragons can’t stop them, if Dothraki and Unsullied and Northmen can’t stop them, how will our army make a difference?
JAIME: This isn’t about noble houses. This is about the living and the dead--
CERSEI: And I intend to stay amongst the living! Let the Stark boy and his new queen defend the north. We stay here, where we’ve always been.
Game of Thrones, Season 7 Episode 7, "The Dragon and the Wolf"
Later in the conversation Cersei and Jaime do mention the yet to come child in a passing moment meaning he knows about it. And yet later at the end they mention it again but it seems as a way of Cersei still trying to manipulate Jaime to stay. When he finally leaves he says "I don't believe you". Now in context this seems to mean "I don't believe you'll kill me" but I think it also expands into the greater meaning of "I've given up on your lies and deception and don't believe you at all anymore". Which then further implies he might not believe her about the child.
CERSEI: Disobeying your Queen’s command. Fighting with her enemies. What would you call it?
Jaime considers his response for a long beat, staring at his sister, his lover, his queen.
JAIME: It doesn’t matter what I’d call it.
He turns to go but finds that the Mountain stands directly in his way.
CERSEI: I told you no one walks away from me.
Jaime turns and looks at her again.
JAIME Are you going to order him to kill me?
Cersei stares at him.
JAIME: I’m the only one you have left. Our children are gone. Our father is gone. It’s just me and you now.
CERSEI: There’s one more yet to come.
Jaime nods.
JAIME: Give the order, then.
He watches her and waits.
The Mountain waits for a command from his queen.
She nods. The smallest possible nod.
The Mountain draws his sword.
Jaime knows there’s no point fighting. He knows he will be cut in half.
He stares at his sister for a long beat.
JAIME: (quiet) I don’t believe you.
After a long beat, Jaime turns and walks away, right past the Mountain and his drawn sword.
Cersei watches. She does not give the command.
Game of Thrones, Season 7 Episode 7, "The Dragon and the Wolf"
Of course this is all pretty much speculation at the moment until the last season but I think the evidence would suggest she isn't pregnant if you look past Cersei's word which isn't really worth much.
It is also worth mentioning that Cersei's prophecy from Maggy only ever mentions three children and so far it has actually been quite accurate.
MAGGY: Three questions you get. You won’t like the answers.
CERSEI: I’ve been promised to the prince. When will we marry?
MAGGY: You’ll never wed the prince. You’ll wed the king.
CERSEI: But I will be queen?
MAGGY: Oh yes, you’ll be queen. For a time. In comes another. Younger, more beautiful, to cast you down and take all you hold dear.
CERSEI: Will the king and I have children?
MAGGY: No. The king will have 20 children, and you will have 3.
CERSEI: That doesn’t make sense.
MAGGY: Gold will be their crowns. Gold their shrouds.
Game of Thrones, Season 5 Episode 1, "The Wars to Come"
The quotes in this answer for "The Dragon and the Wolf" episode are taken from the official script so you can expect them to be as accurate as we can get at the moment.
I believe that it was confirmed in season 7 that Queen Cersei was pregnant.
According to scripts that are publicly available, she is indeed pregnant. Vanity Fair reported on this:
On the first floor of an unassuming building in Los Angeles, there’s a treasure currently waiting for any Game of Thrones fan. The Writers Guild of America West has a library that’s open to the public. In it, you’ll find dozens of scripts from seven seasons of Game of Thrones, as well as other goodies—thanks to the generosity of HBO and, specifically, co-show-runner D.B. Weiss. These scripts and more have been in the collection for years, but flying under the radar. Thanks to a recent bit of social-media-savvy self-promotion, however, interest around the W.G.A. Thrones trove is starting to heat up.
Most of these pages have never made their way online—but after poring over them for hours on end, we dug up several nuggets to share with audiences thirsty for any Westerosi news in the long off-season. What follows is just some of the info we found hidden in between lines of dialogue—in scene descriptions, stage directions, transitions, and so on. And while there are no spoilers here—it can’t be a spoiler if it’s in the script, right?—there are plenty of details that help light the way to what we might expect in the show’s eighth and final season.
The article is obviously spoilerific in some ways, so beware when you visit that link.
With regards to the topic at hand:
Yes, Cersei Really Is Pregnant: There has been a lot of fan speculation that Cersei—who has been known to stretch the truth now and again—was faking her Season 7 pregnancy completely, in order to manipulate both Jaime and Tyrion. However, the show’s script offers no evidence of this. Quite to the contrary: when Cersei first tells Jaime about her pregnancy, the script reads: “She nods, it’s true. [. . .] Her happiness is contagious. They get another chance at family. This time with no one standing in their way.” And when Tyrion later deduces her secret, the script makes it clear that Cersei is caught off guard. Him finding out was apparently not part of some master plot: “Tyrion sees what he sees and knows what it means. He can hardly believe it, but knows it to be true. [. . .] She stays silent for too long, long enough to tell him that he’s right. And once she knows he knows, she can think of nothing else to say.”
Tyrion sees what he sees, and knows what it means. He can hardly believe it, but he knows it to be true. CERSEI Maybe Euron Greyjoy had the right idea: get on a boat, take those who matter-- TYRION You’re pregnant. She stays silent for too long, long enough to tell him that he’s right. And once she knows he knows, she can think of nothing else to say.
– Neo Darwin Jan 07 '19 at 15:41