3-7: Run and Don't Stop
With the Dust King slung over Horse's shoulder like a particularly heavy sack of potatoes, the gang's next move will be to turn him in for his bounty. Each of three major factions—the Holy Nation, the Shek Kingdom, and the United Cities—will pay a cool 35,000 Cats for the man. The most convenient place to turn him in would be the Holy Nation mine just northeast of here on the edge of Skinner's Roam but the Holy Nation can go suck an egg. The gang is taking him to Squin.
Getting from the Dust King Tower to Squin isn't too big an ask. It's on the opposite side of the Border Zone but a squad strong enough to take out the Dust King is surely strong enough to cart him across the ravine. The gang fares just fine. While they encounter some resistance, first from starving bandits and then from dust bandits, it's nothing that gives them too much trouble. In fact, it gives Silvershade a nice, low-stakes opportunity to get used to their new crossbow.

Crossbows are Kenshi's only handheld ranged weapons. There aren't any guns or anything. They work a little differently from melee weapons in a bunch of number-crunchy ways that probably aren't terribly interesting except for one: Damage from crossbows and melee weapons is resisted differently. For example, let's take the chest armour Riddly's been wearing: Standard-grade mercenary plate. It resists 21% of incoming blunt damage, 32% of incoming cutting damage, and has 26 points of “Harpoon resistance”. This means that it negates 26 points of damage from any crossbow bolt (or harpoon, which is the kind of projectile launched by advanced turrets). Silvershade's Specialist-grade tooth pick crossbow does 17-30 damage per shot so as you can see, it'd do next to nothing against Riddly's armour.
The tooth pick's ineffectiveness against armour will be an advantage while the gang fights unarmoured enemies as it'll mitigate all the bolts that Silvershade will be burying in their backs while training up their Precision Shooting skill. When it comes time to take on foes wearing any sort of armour, though—like, say, Holy Nation soldiers just as a randomly selected hypothetical—they'll need a bigger crossbow.
Silvershade's first outing with the crossbow goes well. As they loot the dust bandits who so foolishly attacked them, the gang notices the boss of this little band has a bounty on his head as well. It's 2,048 cats, peanuts compared to the Dust King, but there's no reason not to turn it in as well. Ells picks him up and the gang presses on. They reach Squin in no time.

Hundred Guardian: Peace is dull. Bring me blood.
Hundred Guardian: Watch your fragile bones, flatskin.
“Flatskin” is a word the gang will be hearing a lot if they spend much time in Shek Kingdom territory. It's primarily meant to refer to humans but gets used sometimes on any non-shek. Not a compliment by any means, context usually makes it pretty clear when it's being used in a relatively neutral way or as a derisive slur.
The gate guard can condescend all he likes. The gang just brought in the Dust King when these guys couldn't. Horse and Ells stride triumphantly into the police station with the King and his subject.

Hundred Guardian: [They eye the body on your shoulders]... Here for your reward?
Ells: Yeah... (Hand over bounty)
The guards haul the two bandits up to the third storey of the watchtower where they keep their prisoners, pretty much the exact same setup the Dust King had at his tower. The rest of the gang realizes their two shek members being the ones turning in the bounties probably hasn't exactly helped the way the gate guard looks at them but it is what it is. Earning that guy's respect isn't exactly a priority.
The gang does a quick sweep of the shops, picking up a few odds and ends. It's back to the Hub next; Outlaw Hana fills her arms with research books so she can get cracking on the research when they return. Squin has a pretty typical complement of shops: Weapons, armour, a general store and a couple bars. All shek-owned and operated. Outsiders being allowed in shek cities is a fairly recent development, so few have gained a foothold. In fact, the only non-shek living here seem to be the tech hunters who run the travel shop at the west side of town.
Those tech hunters are about to once again be the only non-shek in Squin at all. The gang gathers together and gets ready to go back to the Hub.

The next three days are spent researching and training. Outlaw Hana learns about things like power generation (wind and biofuel) and cooking while Silvershade practices lockpicking and Cat, Riddly and Burn lug iron back and forth. The others make periodic book runs to keep Outlaw Hana topped up. Also, Pilaf has gotten bigger! She's no longer a pup but an adult bull, ameliorating her stats across the board. I completely missed her becoming a teen—they grow up so fast! Precisely, animals grow from pup to teen at 16 in-game days old and to adult at 24, which is a perfectly sensible sentence to write.
Pilaf has one more milestone to reach—she'll be an elder when she hits 44—at which point she'll be a force to be reckoned with indeed. A very hungry force, mind you, as animals also eat more the older they get. Don't worry, though. Animals in Kenshi don't die of old age. Pilaf will stay with the gang forever unless something terrible happens.
All the while, the gang discusses their next destination. Riddly is interested in exploring deeper into Shek lands next—a new horizon for all and one that will likely lead to all sorts of new places to adventure. Horse points out that they still have unfinished business up north and the advantage of knowing a few places to retreat to if things go wrong up there. Before anyone can roast him about having led the gang north under false pretenses in the past, Jam shocks the gang by suggesting they go north specifically through the heart of the Fog Islands, home of the fogmen.

This is a ridiculous-sounding idea at first blush. The gang already knows the best way north: Go west around the foglands up the coast. Same way they got down to the Hub in the first place. They've heard tales of a city at the core of the foglands, though—not a fogmen city, a people city. The gang's mistake at the Deadhive Overrun was arrogant, Knife's death a tragedy, but they're much stronger now, more numerous, and every last member of the gang can outrun fogmen. Even Pilaf, whose speed as a pup was a major limiting factor for the gang, can gallop along at a comfortable 20mph as an adult. There's no reason they shouldn't be able to reach this fabled city.
It takes the gang some time but they eventually come 'round to the idea. While Outlaw Hana is a little reluctant to leave when there's so much research to do, Cat offers to take her place at the bench. He's got a decent bit of science know-how himself.
So it is that the whole gang minus Cat finds themselves trekking through the eastern edge of Vain, this time not to avoid the Fog Islands but to enter them. On the map above, the Fog Islands are the northwestern region with patches of light grey haze divided by a labyrinth of high ridges.

Rule number one of the Fog Islands is: RUN. Even if you see a small group of fogmen you know you can beat, run. Even if you see someone being eaten alive in one of their deathyards, run. Always assume there are more fogmen lurking just too far away to see.
Soon after the gang enters, before they even run into any fogmen, the map updates with the location of the rumoured city. Mongrel sits right in the middle of the labyrinth. This is good; it gives the gang a precise destination. You can actually right click in the middle of the city once you've discovered it and your characters will do their best to path there; if you do, don't take your eyes off them. Pathing is generally pretty reliable but people can take wrong turns sometimes. They might get back on the right track from there but they can end up wavering confusedly back and forth—a potentially fatal error when being chased by fogmen.

It would be incredibly lucky for the gang not to attract any attention at all in their mad dash through the foglands and today is not that day. While climbing a hill next to a huge rusted derelict frame of some sort, they end up with a group of pursuers. The gang could defeat them easily but: Remember rule number one. They keep running up and down hills, through the foglands' twists and turns, until they can actually see Mongrel's walls. Then, they turn. So close to the safety of Mongrel, the rules change, and the gang cuts the fogmen down with little issue.

Rule number two of the Fog Islands: Don't do the exact thing Burn is doing right now. Don't go chasing after a distant prince you can only just barely glimpse through the fog. They're lucky that the rest of the gang is pretty safe right now; I can afford to watch closely enough to make them run back at just the right moment before they get into trouble.
This actually ends up being a nice little surprise boon. Burn runs back to the gang once they have the prince's attention, bringing them and their heavies to where it's relatively safe to fight. The gang knocks them down and takes the prince's head, another 6000 Cats in their pocket from the first shop they walk into in Mongrel.
The gang approaches the gate. The guards here are black-clad ninja in fog masks just like the one Riddly wears.

Shinobi Guard: A new guy, eh? Must be tougher than you look, making it here to the city in one piece.
Jam: What can you tell me about this place?
Shinobi Guard: People don't make a habit of visiting here. If you're lucky enough to make it to Mongrel, you're stuck in Mongrel. The plus side? No one will find you in this town... If you got someone to hide from, that is. 'Round here you'll find mostly outlaws and ex-slaves.
Jam: Stuck here, huh... Any survival advice?
Shinobi Guard: If you're staying? Keep your head down. If you're heading out? ... Well, you should avoid the Deathyards altogether. The mist tends to... swallow travellers up, shall we say?
Shinobi Guard: Same goes for the floodlands up north. If you make it out of the mist, that is. People who go to the floodlands... they don't come back.
Jam: What happens to people in the Deathyards?
Shinobi Guard: No one really knows. Some reckon it's to do with evil spirits, and then you got others who believe in the curse of the mist: people get lost, lose their sanity and starve to death...
Shinobi Guard: People here—the ones that haven't lost their minds, that is—they don't talk about the fog...
Jam: What about the Floodlands?
Shinobi Guard: A place where adventurers and treasure hunters go and never come back from, like always, the idiots. Some say the killer machines get to 'em...
Shinobi Guard: But me? ... I reckon all those missing people saw somethin' they weren't supposed to see...
Jam: Any way I can earn some money around here?
Shinobi Guard: At the moment, no, jobs are dry. Come back in a few months, eh?
You might think that simply standing in the fog would have some horrible gameplay effects from the way the guard talks about it and considering the fog mask's description says it "helps mitigate the negative health effects of fog" but it does not. Where gameplay is concerned, the presence of fogmen is the only thing that makes the fog dangerous.
On that note, the Deathyards are scattered camps throughout the foglands where fogmen take people to eat. They're not much to look at, appearing to be nothing more than a few sticks stuck in the ground, some for chaining up victims and some decorated with said victims' skulls. The horror of them comes from the screams of the victims being eaten there, a sound Mongrel's residents have to hear far more often than anyone should. The gang hopes their contribution to fighting the fogmen helps make at least a few screamless nights.