East coast jumper is spot on.
You need to figure out why the tank vent has a filter and no one way valve. First off no need for a filter there, fuel does not flow through it. And you need the one way valve to make sure the fuel system can pressurize.
The second pulser fitting that is plugged with a bolt should be done correctly. The bolt may leak and you don't want a crankcase air leak.
The blue vent is for the battery as others mentioned. I got rid of the wet battery because it was spewing acid out at the bottom of the handle pole. Unacceptable. I went with a Yuasa AGM instead, way better.
The ski generally sits to the right due to the battery and fuel tank biased to that side, I doubt its from that small weight in the front.
Yes, steering cable needs to be replaced. Looks more like rubbing than melting. The steering cable lays along the waterbox in that same spot in both my skis.
Edit: Can't vouch for the quality but Thrust has steering cables on sale. I would want OEM or a heavy duty.
https://www.thrustinnovations.com/index.php?main_page=product_info&cPath=&products_id=1361
As others said the carb bracket just doesn't have anywhere to go because that is a different cylinder head. You could pick up an inexpensive 61X head around here or eBay if you wanted it to be right.
Here are a few photos of my engine bay so you can see a few of those details. The second pulser fitting is not tapped on the 62T cases.



