When Kate is underwater, keep going to the right and stick to the wall - after just a few steps you will encounter a large, circular recess with a valve and several bolts inside. Pick up the large cog (on the left) and the square key (on the right). Zoom in on the recess. You will see two more cogs, right underneath it, which you should also collect.
Install them onto the bolts: the large one on the left, the ordinary one at the top, and the one named the gearwheel (which looks a bit different than the others) below them.. If you have the commissar's note, you can check in the documents inventory, that the chain is still missing. You have to go further and find it.
Keep going to the left, changing the route only when Kate gets stuck somewhere (go down on the screen a bit to avoid the obstacle, and then continue going to the left). This way, after some time, you will reach another large metal hatch on the wall to your left - approach it, to perform the necessary operations.
Open the first lock
In order to unlock the hatch, place the square key you found by the first recess into the hole under the valve, and then turn it to the right (with the correct mouse movement). The hatch will open up a bit - you should open it entirely (by moving the mouse from the right to the left side, the active point is located left of the valve).
A recess with cogs and a chain will be unveiled - turn (with the correct mouse movement) the valve to the left as far as possible, and then pull the lever (with the correct mouse movement) on the left down.
Go through the open gate (on the left). Take a few steps to the left when the perspective changes, and then a few more towards the middle of the screen, where the wreckage of a ship is located. Take the chain, which is lying more or less in the middle of the debris.
Go back through the gate and keep going right (it might take a while), in order to reach the other recess with the cogs, the one with the missing chain.
Open the second lock
Place the chain between the valve and the lower gear (the active point is on the left of the gear to which the valve is attached; if you have not put the gears in the correct positions yet, the picture above shows where exactly they should be placed). Turn the valve to right as far as you can, and then click on the lever on the right (you will receive the achievement 20,000 leagues under the lake).
When Kate is at the police checkpoint, , look inside the building through the window on the right of the door (Turning the tables achievement) and then run to the Youkol tent. When you are there you must pet the third ostrich on the left of the entrance (required for an achievement). Next, you must go to the shaman's quarters - inform her that the nomads can go through the lake.
Return to the ferry and head towards the exit from it, and then discuss the situation with Sarah and Ayawaska - Kate will receive a wineskin from her with the shaman's beverage.