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If am not wrong that's the drainage pipe to throw out excess petrol or water seepage through petrol tank cover?? If you look carefully, there will be hole/s just around the the rim of the petrol tank once you open the tank lid. In case of full tank, any spillage will be thrown out. Also, during rains / wash, if any water dies seep in through the key hole, it gets drained out through that hole only.
Not very sure :P

It is a drain pipe. Generally there are two to three. One for carburettor and Battery.
Not to worry.

rx100.7050 When i checked its hanging directly over the hot engine (overall assembly is like that). If its leaking oil then its not good. The manual has no info about the carb but its written keihin on it. I'm trying to google it for more info.

Nothing to worry boss. Its the drain pipe from the petrol tank. It collects water from the petrol tank cap and throws it outside. You can see it working during monsoon. Moreover, the water evaporates from the hot engine walls almost immediately. Chill and keep riding.

Generally every bike has at least 4 drain pies, some can be easily seen.

1. Drain pipe from Petrol tank to drain the water seeped through fuel filler cap. Esp useful in monsoon and pressure wash. Always make sure this hole is unclogged.
2. Drain pipe from battery to dispose off extra acidic water and fumes.
3. Drain pipe from the bottom of the carb, to dispose off the water entered in the carb
4. Drain pipe from the air filter box t dispose off the water, collected because of moist air and rain ( monsoon)

You have asked about no.3 pipe
Many times due to water seepage in the tank, petrol brings some water along with itself in the carb.
Water being heavier, is collected at the bottom of the carb. If there is too much water in the carb there won’t be any space left for the petrol and instead of petrol water will be sprayed in the intake manifold (or engine), causing misfire to even seizure.
There is a screw which allows the contents of the carb sump to be released, through this drain pipe.
In monsoon and after a pressure wash, if you fill the engine is not starting because of water in the system, slowly unscrew this screw and check if any water is coming out.
Also avoid riding on RESERVE, coz this accesses the bottom most part of the tank for fuel, which might have some water, seeped through the filler cap.

Even the carburettor has 2 or 3 tubes.Those would be:-

Tube 1 - Air vent connecting hose of carburetor.The air vent's purpose is to maintain the pressure inside the fuel bowl.If it is not there it would result in increase of pressure due to fuel vibration.The hose purpose is to prevent dust from entering inside the air vent.

Tube 2 - Fuel drain hose - To drain the fuel in the bowl for clearing water or dirt.

Tube 3 - Overflow Hose - To put out the fuel in case the needle valve(Allows fuel inside the bowl and closes the supply when filled) or the Float is faulty.

What navaroj said.

What you've found is the float bowl overflow. It allows fuel to run out of the float bowl if the needle valve sticks open. It's a bit "oily" because every now and then a drop of fuel will splash up into the tube and weep out the end. It's nothing to worry about.