(Spoiler Main) What will happen to the white walkers?

First post here, I hope I don't break any rules.

So my question is, are there any more detailed and thought-out theories on what will happen at the very end to the white walkers? If not I would like to know what your thoughts about how the war against them will go are. I believe it is commony agreed upon that the wall will somehow fall but what then? Will the whites come as far as kings landing or maybe even further? How would you assess the significance of Valyrian steel and dragonglass in the war?

Other questions:

• item 1 Will the lords of westeros at some point unite against the common threat?

• item 2 How fast can the white walkers advance?

• item 3 Are they all going to be killed in the end or can/will the war end in any other way?

Please share your thoughts or post exisiting theories if you know any.