No. Faire is the French verb which means to make or to do. It is part of quite a few set idiomatic expressions which is why it will sometimes have some unusual translations. But here it just means make. Brewing is the process generally used to make the beverage coffee, but it is not a synonym. To make the name of a process for making something the synonym for make would require a LOT of synonyms for make like bake, build, mold, construct, sew, manufacture, etc. It is important not to mix up synonymous with having the same end meaning. In learning a language, we are learning how grammar, syntax and semantics work together to create meaning.
Faire is an irregular verb. It is one of the few that have irregular vous forms.
In the French imperative, as in the English, the subject pronoun is omitted. Otherwise the verb forms are the same, except the tu form loses the s at the end in er verbs and some others. If there is an object pronoun it is attached with a hyphen in affirmative commands (Donnez-moi or Donnez-le-moi) In negative commands the object pronouns preceed the noun as in other sentences.
Not everyone goes to the trouble of brewing coffee when they make some coffee. Sometimes they just put a teaspoon of instant coffee into really hot water.
I suppose that technically you could call it brewing but it seems misapplied. Most people would think that when you said you were brewing some coffee, that you would come back with something more than instant coffee.
Du is a partitive article used before masculine nouns. The closest English equivalent would be some. In French this partitive is required when speaking about unspecified singular quantities. Most of the time you could use the word some in the English sentence, but it wouldn't be required.