OK - so I found another diagram that shows where the tube routes - round to inside the black plastic as the back, with the tubes going down to lower in the case..
Still unsure *why* that might have been disconnected / is missing, could just be someone forgot to put it back, but maybe they didn't want air routing that way?
Unsure about the purpose of tube marked 10 on the original diagram still as well, can't see in diagrams where that would route to
That breather hose directs crankcase gasses to the engine intake so that they can be burned and help keep emissions to the atmosphere in check. Depending on the outboard's age and condition, it may have deteriorated and not been replaced. Or, it could have just been left off from a careless reassembly job. It's good for the environment to keep that breather hose and system in place. It will also keep crankcase oil vapor from spraying around under the engine cover and making a dirty mess.
The #10 bulk hose you ask about is simply a drain for the muffler cover housing. It connects to a nipple at the bottom of the muffler and routes to a small channel under the muffler to drain any vapor condensation or water out the bottom side of the engine compartment. This is important in that any liquid held in that space could be ingested through the intake and possibly damage the engine.
You will probably find the "flame trap" screen (item 1 in your first link) either missing or laying in the bottom of the muffler when you open it up. Those come loose when normal engine vibrations cause the little plastic "ears" that hold it in to deteriorate. I have remedied that by using a very small (#4) sheet metal screw to wedge it in place from the bottom. It's a "quick n dirty" solution that you might want to improve on. Replacing the muffler is the factory fix but expensive.
