the little hose is your vent hose that comes from the motor to recycle waste oil... just make the tube run down like the fuel overflow from the carb to below the bike and you should get a little better performance without the hose connected to the filter, that what everyone does with the...
for this bike do not go over 26mm carb, you would do good with a 24mm carb.. on amazon look up nibbi carburetors and they have the carbs preset for certain sized motors to get you in the ballpark for running, they also come with spare jets to help get it running just right
looks like a lifan 110 to me, there is a vin number on the head tube of the bike you can use to get the manufacterers( lifan,zongshen,etc). take that info to vindecoderz.com and they can give you info on make and model possibly
For your motor that is a large pilot jet,second screwing the air/fuel out will lean out the lower the amount of fuel by allowing more air in, try turning it out to 3 and see of that helps is my best guess, hppe this helps