The adjective powerful can refer to physical strength (a powerful athlete), great effectiveness (a powerful speech), or high potency (a powerful drug). But powerful overlaps with mighty only when describing people or entities that have great power, authority, or influence (a powerful nation). Mighty is chiefly used in a rhetorical manner to indicate uncommon or overwhelming strength or force (a mighty army). Though you might encounter it describing things of uncommon or overwhelming size (a mighty oak; a mighty river), or, things that are great in amount, extent, degree, or importance (a mighty accomplishment).
To confuse someone is to perplex or bewilder them (the flood of questions confused me). To befuddle someone is to confuse them, especially with glib statements or with baffling behavior. The suggestion bundled into befuddle is that of making the mind slow or foggy, as from intoxication, a connotation inherited from the verb fuddle, meaning "to tipple," that is, to drink intoxicating liquor, especially habitually or to some excess. Fuddle entered English nearly 300 years before befuddle, which explains the boozy nature of befuddle's earliest meaning in English: "to make stupidly drunk."
The verb want is one of the most frequently used verbs in the English language. It conveys desire in ways ranging from the more casual (she wants an ice cream) to more intense (she wants to be notified in case of emergency). Covet also deals with desire, but more specifically, it deals with the desire to possess what someone else possesses (she coveted her friend’s beachfront property). Envy and longing are implied by this term, though covet is sometimes used in a less grasping manner to talk about wishing for something eagerly.