When people use the phrase "by the skin of your teeth," they mean that the person barely accomplished what they were trying to. The figure of speech "skin of your nose" is not a common one.

Yes you can, but stop if it's beard gets dark or if it kind of tries to get out of your hand STOP, because that means it doesn't like it. Also only pull the skin if it's hanging or if the skin is on it"s nose. If the skin on it's nose it can't breathe!

because the skin in your nose is very sensitive so when you pluck your nose hairs it can rip off a large amount of skin that is why its bad to pluck nose hairs

that is actually incorrect. its a combination (most likely due to confusion) of "by the skin of my teeth" and "its no skin off my nose." not sure how either of those got started, but just fyi

no skin off my nose