What can we say about the internal state of the Westerlands at the end of ADWD? To what extend did Tywin’s death weaken Lannister rule over their vassals? Could you see a scenario, where the western Lords rebell against Cersei?

It’s certainly weakened; a large part of Lannister control over the Westerlands was about the personal legend of Tywin, the Rains of Castamere, and so on. 

I don’t know about rebellion, but it doesn’t help that the Lannisters are starting to become absentee landlords in the Westerlands, so focused on maintaining power in King’s Landing that Casterly Rock is beginning to become an undesirable posting.