I watched the first season, way back when, but never followed it through. So I might be as lost as you are. However, this is my take on the sequel:
Agent Cooper must have disappeared or died in the original series. Part 1 - 2 shows where he has been since that time, and Part 3 - 4 shows his emergence back into our world. They are not robots. He is in a world where communication is facilitated through a tree spirit that takes on images that are familiar to Cooper. Like Laura Palmer. "Sometimes my arms bend backwards," like a tree taking the wind. She told him that he has a doppelganger who must come into that mystic world before he can be released back into our world.
There does seem to be a portal into our world and it is being watched by the military. So, far, Agent Cooper has found his way to the door of the portal, and so has a black cloudy evil that broke the glass and attacked the guy whose task it was to watch the portal to see if anything appears. Wouldn't you know it, it picks the moment that the poor guy is making out with his snoop girlfriend and may have killed them. Now, I don't think that these appearances happened in real time, so they only confuse the story telling.
What we do know is that Agent Cooper did find his way back at about the same time that his Doppleganger, Doug, has a car accident. Doppleganger Doug appears to live past the accident, long enough to get nooky from a prostitute before he gets sucked into the mystic world, and Cooper's soul reappears into our world through a power outlet and materializes as Cooper. Except, he is a blank slate. He probably has no memories, because he doesn't even know he's supposed to relieve himself when the urge hits.
What he is good at is triggering the one arm bandits at casinos. He makes a lot of money, attracts attention of friendlies who know him as "Doug the Doppleganger" and they take him to Doug's house. His wife doesn't seem to be perturbed by his walking coma, probably thinks he went out on a bender.
Meanwhile, Doppleganger Doug, geez, hard to explain. One part of him gets dematerialized into a ball bearing in the mystic world, but he still seems to have a corporal body because he communicates with the military through that portal.
The end of part Four leaves two in the investigative team trying to make sense of the cryptic conversation with Doppleganger Doug, who they think is Agent Cooper. Good luck with that.
I'm thinking that Twin Peaks is a social experiment to see just how addicted the U.S. population is to watching t.v.
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