1. As long as that hose is inside the airbox and making a tight seal you're fine. It's part of the EGR/PAIR valve system that takes air from the valve cover to be reburned. It's fine.
3. that's a similar vent hose from the transmission, again it's fine.
Just to the right of 3 there's a tiny drain opening. It has some foam in it and looks like the plastic slat in the photo runs into it. It should attach to a hose that runs to a tiny catch bottle located behind the right footpeg cover. The bottle has a tiny drain plug in the bottom for when it get's filled. It's almost impossible to see unless you know where to look for it.
Neither 1 or 3 are the outside open vent lines. There are 4 of those and they attach one to each carb and one up under the other one goes up under the fuel tank. (The other open hose from the fuel tank is the water drain / overflow drain for the filler cap.)
Oil is not uncommon in the airbox, especially if the gearbox was overfilled. You are in fact supposed to oil the OEM filter. That's also why there is a catch bottle.
As for putting in a K&N filter, there are instructions on modifying the airbox for them. I think it involves drilling extra holes. I'm not convinced this is needed, nor will it help your issues.
As per Hugo's comments the tiny fuel filter in the T fitting is stock and as log as clean won't cause any issues. It's there to prevent a blocked carb jet.
The majority of carb issues involve 1. dirty carbs and clogged jets 2. air leak or 3. incorrect adjustment of pilot air jets. It's also important to know you can't really get the bike to run properly with the airbox open and the filter out. You need some of that back pressure to help draw the fuel up from the carb bowls.
Here's a thread showing some info I posted about carbs. Also shows the air needles.
Alright guys, ? I had posted a thread about selling my ZR7-S fairing because I decided to go full naked with the ZR just wanted to show off some as I am pretty proud of the result, the Gauges are from a ZRX1200, the headlight bucket is an OEM honda bucket with unbranded brackets (bought used...
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