[asesh]

'Nose' is a smelling organ. 'To have a big nose' means extra inquisitive. Absolutely right.
'Running nose' is having cold (something to do with nose). 'Having a parrot nose' is more to do with nose appearing like parrot.
Speaking through the nose: Nasal accent. (Again about nose)
Has a good nose: sense of smell (dogs)
Nose dive: Aeroplane's plunge from front.
Others like:
As plain as the nose in your face: easily seen.
Cutting off one's nose: Humiliation.
Making a long nose: person not in agreement
Pay through the nose: Overcharged in price
right under one's nose: right in front of

So nose is a vital organ of us. Like blind, deaf, dumb, one who is incapable of smelling anything is called ......
Please help.
Asesh