Can I use 'nose shit' to mean 'bogey' and 'snot' and 'mucus'? Then what is the formal and informal words for 'nose shit'?
And how about the word for 'eye shit'? what is the formal and informal words for 'eye shit'?
There is no such thing as "nose shit" or "eye shit" unless you wish to appear extremely childish or crude.
With respect to your nose, you have mucusas a polite word and bogeyand snotmeaning the same thing in a slang, slightly crude way. (you would usually not refer it as such with your mother or someone that you otherwise respect.)
If the mucus is liquid and uncontrollably coming out of your nose, as happens when you are sick, we say "Your nose is running"
With respect to your eyes, the liquid is called tears. In the morning you may have hard bits in the corner of your eyes...we call that sleep as it only forms when you are sleeping.