If it's dribbling mayonnaise that sounds it's like a drain from the air box. The crankcase breather can blow emulsified oil and condensation into the box, at this time of year the cause is probably just oil temperatures not getting high enough to evaporate the moisture but it is always worth checking coolant level to make sure.
You wouldn't get that stuff coming out of the fuel tank breather, it would only be fuel. Airbox gunk looks like liquid honeycomb.Why the pipe is shredded is a bit of a mystery though.
I wouldn't mind betting that a reasonably sized motor factors could supply piping that size in a clear plastic/nylon type material for a fraction of the price of the Yamaha replacement pipe and the plus side is you can see what is actually in the pipe being clear/see through.
Perfectly ok to me, just check the spigot on the airbox where it fits is 8mm as well.