I'm betting that a pWhile there is still a Lannister army, as Jaime told Cersei, they would be easily destroyed by Dany's forces (the Unsullied, Dothraki and dragons). That's why Cersei needs the Golden Company for the next battle - whatever that may be.
I believe you recall correctly. Her plan seems to be let the others fight the Whites. If the Whites win, she is screwed anyway. If they don't, she is dealing with a weaker opposition.This is a good question - correct me if I'm wrong: Cersei agrees to help in the great war and tells Tyrion she's sending her army north, but that's not true, right? She tells Jaime she's not actually sending the army and thus, the reason he heads north (is that right?). So, Sansa's jab at her HUSBAND Tyrion is spot on - he's a fool for beliving Cersei.
To that end, I have no idea what her plans appear to be. My guess is attack the other armies when she gets a chance? She's sort of all over the place.
Will be interesting how this all plays out, but yes, Tyrion should know better. He does know Jaime is a man of his word. And he thought she is pregnant so as he said: she has something to live for. Pretty dumb to say publicly that the Lannister army is coming. That might bite him in the ass. Just another thing for Dany to have to overcome with people of the North.