Think of a kalpa as your computer before you wipe the drive. Once you wipe it and reboot it, it starts a new kalpa that lasts until you decide to wipe it again. That's what Mundus is (or the entire TES universe, I'm not exactly sure on that part). Alduin's job is to reset everything (hence, World Eater) but one time he got power hungry and decided to rule over the kalpa rather than reset it.
That's about all I could tell you without delving into even more metaphysics. I'm not well-versed in the lore to answer the other stuff (though my basic understanding of the Amaranth is basically someone who reaches a high enough metaphysical awareness that they are able to transcend this reality and dream up a new one, therefore becoming their own god of another plane of existence).
Kalpa is like a world cycle. The first poster gave a nice breakdown. Basically, Alduin/Sakatal eats everything and creation has to happen all over again. We don't actually perfectly understand it though and there are plenty of questions left to be asked. Such as, how high up does the reset go? We're lead to believe that it includes the Aedra and Daedra, but what about Anu and Padomay? (I personally think it can't go that high, its just the Aurbis that resets.) How similar/different is each Kalpa? One source (which may be developer written or may be really good fan fiction) leads us to believe that the Daedra of this Kalpa become the Aedra of the next Kalpa.
Landfall is some sort of catastrophe on a universal scale. Its what Amaranth is trying to save us from. We actually don't know that much about it yet, but apparently we'll find out soon (text incoming.) It could be that by stopping Alduin, the Last Dragonborn upseat the Kalpic cycle and that's why Landfall is coming.
Yes.
Amaranth is the final state. Its what happens when you have a complete understanding of the fabric of the universe. You go to sleep and, out of love, Dream up a whole new world.
I thought it was the reverse? I thought the source implied that one of the Princes used to be in charge.
It'd be interesting if the reason the Daedra don't participate in the creation of Mundus is because they were the Aedra of the previous cycle, and know what happens to those who do. Personally though, I'm still leaning more towards it only going back so far as the creation of Mundus (though I admit I'm not particularly learned, so I go with what I'm comfortable with right now and I can't really fathom it going higher).
It'd be interesting to have the events of Landfall be the storyline of a TES game, though it'd have to include all of Tamirel to make it satisfying, so I'm not exactly holding my breath for it.
Interesting.
My personal view of Kalpas is what's in the http://www.uesp.net/wiki/Lore:The_Annotated_Anuad:
12 worlds = 12 previous Kalpas.
Padomay's sword = Alduin
Clearly Anu is more Lorkhanic here wile Padomay is Akaic (lol...Akaic). Anu's defending creation like many a Shazzarine and then Padomay strikes his heart to seal the deal.
I actually never realized the irony of Anu, the father of Aurie-El.. being the dreamer of the world the Thalmor hate.
Actually, Anu is the father of existence as we know it; the dreamer of the world (Mundus/Nirn) was Lorkhan, whom the Thalmor hate.
So then wasn't it Anu who dreamt up Lorkhan?
I'm actually still not completely clear on Amaranth. So was it Godhead dreamed up Anu and Padomay, then Anu dreamed up a separate universe which was interrupted by Padomay, or was it that Anu dreamed the Aurbis and all it's denizens after the Godhead dreamed him?
As an aside, I recently dreamed that I couldn't resist falling asleep. I grew terrified of what would happen if I double-slept, so woke myself up. I wonder what could have happened if I had slept in my dream?
A Kalpa is a parabolic unit of time.
Landfall is absolute mortal z.
C0DA will be along shortly.