What are Cersei's intentions throughout this interaction?

Question

In "The Dragon and The Wolf" (Game of Thrones, S07E07), Cersei

1) announces her disbelief in the Night King, 2) changes her mind when she sees the wight and sees Euron flee, but it is later revealed that this was planned, 3) demands Jon remain neutral after the war against the Night King, 4) refuses a truce after Jon refuses her demands, but is then convinced by Tyrion to accept the truce, and 5) turns out to not accept the truce after all, and intends Daenerys and Jon to fight NK alone.

What are her intentions and plans throughout this interaction?

It seems very confusing to me. Her action number 1 and action number 2 seem to conflict: if she didn't believe in the Night King army, how could she have planned for Euron to pretend to betray her in the first place? If she did believe in it, why did she pretend not to?

In action (3), she demands Jon not choose sides if Cersei is to help them in the war. But, as she reveals in (5), she never intended to join them in the first place. So, what was the point of asking Jon to not choose sides? Even if he agreed, the moment he realizes Cersei's betrayal, that oath automatically becomes null, right? Because Cersei didn't keep up her end of the word, why should Jon?

Finally, Cersei's plan is to make it seem as if she will join them, when, in reality, she won't (5). But why did she agree to meet with them at all then? What is the point of pretending that she will join when in reality she won't? Even if she flat-out refused them, wouldn't the same conclusion be reached? Jon and Daenerys would march North, and Cersei would stay behind. Same result. Her "betrayal" wouldn't come as a surprise either, since Jon and Daenerys would immediately realize it upon arrival at Winterfell, where a raven would presumably inform them that hey, the Lannister army is still at King's Landing.

So did she only agree to meet them in order for this entire episode to happen? What other reasons did she have?

Answer 1

The only thing I don't understand is

taking back the lands

since I am not sure that Daenerys is actually holding any lands after she won the battle. I just thought she destroyed the army.

Anyway, it is not conflicting what she did. It was putting up a good show that will convince Jon and Daenerys to trust her with truce. After the defeat, truce is in Cercei's interest so she can prepare herself again. If she just said "Ok I agree to truce", nobody would believe her. And if she really rejected the truce because of Jon, she had no reason to spare Tyrion. It was all acting.

1) and 2) are not conflicting. Nobody believes in Walkers, but if Daenerys is willing to post-pone the war she is winning and especially if Jon is going to appear in King's Landing, then she understands that there is something to it. Plus they wouldn't come without the proof. So she has to let them prove her wrong in order to get the truce, but in any case she needs Euron to sail to Essos, this is just a chance to cover that move.

Asking Jon to stay neutral is the least they expect her to try to weaken Daenerys. Like I said, simple acceptance of truce will be more suspicios, and therefore may influence Danny to leave some troops behind or to monitor Narrow sea. She deosn't care will Jon be neutral because after all the fighting, entire North can't put up a decent army and won't make much diifference. Afterwards she lets Tyrion understands that she is pregnant and that actually fight for the living is what she really wants because he knows how she loves her children. If she wanted to hide that from Tyrion she would have never placed her hand on her belly. Afterwards Tyrion is 100% certain she is joining the fight because of her unborn baby. She declares joining the fight without assurances which means she is aware she can't win the war against Dragonqueen. She played it all and made them fully convinced she means to fight the dead, hoping that will bring safety to her baby and save her own skin because there is no other way for her really.

The fact that she is not joining the fight also tell us that even after seeing the wight she still doesn't understand how dangerous the Night King really is. Truly enough, Jamie is kinda naive to believe that some white monster has 100k soldiers north of the Wall just because the enemy told it to you.

Other questions... even if Cercei's backstabs Danny, Jon will remain neutral if he gave his word that he will, but like I said, I doubt it was attempt to separate their armies since she has no reason to be afraid of Jon's army. She probably expected Ned's son to respond that way when Danny is already agreed to save the North.

She met with them to really convince them that the truce will hold. She needs time anyway to get mercenaries from Essos, recruit more youngsters in Westeros, perhaps build more devices to fight dragons too. If she didn't, Danny might decide to burn the Red Keep first, even though she would look like destroyer, but most of the city would remain and those who die are necessary vicitms to go and face White Walkers without leaving her back open. Danny doesn't like doing it, but in this kind of circumstances she might decides to do it regardless of advices. Furthermore, Cercei would do it, so in her head Danny might also do it. So it is better to ensure the truce and buy yourself a much needed time.

Answer 2

She says it herself at the end of the S07E07, in the conversation with Jaime:

The monsters are real. The white walkers, the dragons, the Dothraki screamers... all the frightening stories we heard when we were young, they're all real.

So be it.

Let the monsters kill each other. And while they battle in the North, we take back the lands that belong to us.

Also, this conversation with Jaime from S07E05 let us know about her intentions:

Jaime: You let it happen (note: the secret meeting of Jaime and Tyrion). Why?

Cersei: I've come to believe that an accommodation with the Dragon Queen could be in our immediate interest. She has the numbers. If we want to beat her, we have to be clever.

This means she plans to trick the Dragon Queen. Both these conversations give answers to your points.

She does indeed believe in the Night King (and the other "monsters").

She tries to tie Jon Snow's hands by making him extend the truce - very clever move, because she knows Jon Snow would keep his word. That way, she would then face smaller army. Jon refuses though.

She then tricks Danaerys and Tyrion by promising to keep the truce and even participation on fighting the Night king, while she prepares to attack them instead.