It is the section just right of Main Street.
The monsters on Steamworks are all mutations of plants on the island. They took over the island after being altered in the Research labs (Production Zone) to the right of the Hub. You battle them at several locations on the island. (see related question)
on the hot hatch on the hub place all the way on the right
The "rope" is a coil of old vine on the roof of the , left of the Living Quarters. You need it underground at the Hub.
In the underground below the Hub, you use it to rope a steam pipe to knock out an attacking monster in the pipes.
To get to the drawbridge, you go to the right of the Hub all the way to the edge of the scene. You get the key for it in Captain Ziggs' cabin.
There is a loop of old vine on the roof of the building at the far left of the island, past the Living Quarters. You should get it early because you will need it at the Hub.
The number is on the typewriter, "516". It is the combination (0516) to the secret room in the Captain's Quarters atop the Hub.
It is at the upper left side of the Hub. You will have to go underground by having Sprocket drop the Robot Crab on the hot hatch. Once power is back on, throw the lever at the right side of the Hub and ride it up to the top, then go left to find the elevator.
The steam battery is in the trash bin at the right of the Cantina. You need it to open the doors (Sully's, Living Quarters) and lower the Bridge at the Hub.
The robot crab is full of cold water, which you can use to cool down the Hot Hatch at the Hub on Steamworks Island. However, you will need Sprocket the Robot to help you. Find the robot at the Living Quarters to the far left of the main part of the island. Jump on him to get him and Sully's door key. Using the Steam Generator (trash bin at the Cantina), open Sully's door and find Sprocket. Ringing the bell on the counter will awaken him. Take him and the crab to the Hot Hatch at the Hub. Use the robot crab and Sprocket will drop it on the Hatch, cooling it down so you can go underground. That is the only use for the crab
The robot crab is full of cold water, which you can use to cool down the Hot Hatch at the Hub on Steamworks Island. However, you will need Sprocket the Robot to help you. Find the robot at the Living Quarters to the far left of the main part of the island. Jump on him to get him and Sully's door key. Using the Steam Generator (trash bin at the Cantina), open Sully's door and find Sprocket. Ringing the bell on the counter will awaken him. Take him and the crab to the Hot Hatch at the Hub. Use the robot crab and Sprocket will drop it on the Hatch, cooling it down so you can go underground. That is the only use for the crab.
The robot crab is full of cold water, which you can use to cool down the Hot Hatch at the Hub on Steamworks Island. However, you will need Sprocket the Robot to help you. Find the robot at the Living Quarters to the far left of the main part of the island. Jump on him to get him and Sully's door key. Using the Steam Generator (trash bin at the Cantina), open Sully's door and find Sprocket. Ringing the bell on the counter will awaken him. Take him and the crab to the Hot Hatch at the Hub. Use the robot crab and Sprocket will drop it on the Hatch, cooling it down so you can go underground. That is the only use for the crab.