what are the differences between
gebrauchen,
aufbrauchen,
verbrauchen,
nutzen,
benutzen,
ausnutzen,
benützen,
anwenden, &
verwenden?
my dictionary gave me these translations for the word 'use' :,)

difficult :) I'll try to give some distinctions:
gebrauchen: mainly used to say 'I could use X' = "Ich könnte X gebrauchen", in the sense of I'd like to have X
aufbrauchen: to use something (e.g. some material) up, leaving nothing behind
verbrauchen: to consume. Like aufbrauchen, but not necessarily leaving nothing behind. For example used for using energy
nutzen/benutzen: general 'use', but benutzen is negative when used with people. E.g. 'jemanden benutzen' can mean to exploit or even abuse another person
ausnutzen: can mean to use some opportunity, e.g. 'das gute wetter ausnutzen' = 'to take advantage of the good weather', but with people it's similar to benutzen: negative, but more in the 'abuse their generosity or ignorance' way
benützen = benutzen
anwenden: use a method, mathematical rule etc. to do something
verwenden = use some tool to do something

hope that helps a bit :)