The opening scene of "Chapter 18" is the most aptly nonsensical scene in the history of this show, because from here on out, things are about to get a clear as mud. Our first introduction to Frank Underwood's practically unintelligible adventure is a scene in which a strange man plays out some bondage-asphyxiation fantasy with a duo of prostitutes. Later we see him pay the man and woman a lot of cash. But do we get any information? Nah. What would we need that for?
With even less explanation, we find soldiers reenacting a Civil War battle as Frank sits idly by in a pseudo-throne, waiting to give a speech which will inevitably serve as an excuse for him to make an aside to the viewer. He makes some comment about weirdoes fetishizing the Confederacy when they supported slavery and moves along. Why's he there? Nobody knows.
Meanwhile, Claire is working with a plot that makes sense: Connor knows her abortion happened five years after her rape and he's worried that someone will find out. She's not, but that just means she definitely should be. Learn the rules of House of Cards, Claire.
After that aside, we find out why Frank is at this silly reenactment: it brings him in contact with Xander Feng, Chinese Telecomm billionaire and an apparent fan of potentially-fatal sex. Feng has been inserted into the U.S.-Chinese summit and he's friends with Tusk, which means having Feng around isn't ideal because it probably means that Tusk is just looking to line his own pocket. Cherish this moment because it's the last time this poorly-explained plot will be intelligible.
Then -- to fulfill the purpose of the trip -- Frank meets with Feng. Without giving us nearly enough context about all the ridiculous details traded between Feng and Frank, we're dunked into a tank of diplomatic mines that sort of boils down to this: Feng is behind Chinese investments in a U.S. refinery and a bridge over the Long Island Sound. President Walker is tres stoked about that bridge and Frank wants to make sure he gets it. But Feng is bored with bridges. He wants to talk lawsuits, specifically the U.S. not dropping a lawsuit against the World Trade Organization so it can look like China was forced out. This is weird, because in a normal world, dropping the suit would have been the nice thing the U.S. does so they can have their bridge. I'd attempt to go deeper, but you're going to need your brain intact for the rest of this.
Naturally, Frank thinks Feng is lying about the WTO lawsuit and that Beijing is probably still down with the U.S. dropping it: he thinks Feng is backchanneling to his own ends so he wants to leak that a businessman is involved in the talks without saying it's Feng, the idea being that if Feng is full of it, it'll become obvious.