That walk to go down to Egypt - Hebrew, ‘Going in the descent to Egypt.’ That is, they do it by their ambassadors Isaiah 30:4. The journey to Egypt from Palestine is always represented as going down Genesis 12:10; Genesis 42:3; Genesis 43:15; Numbers 20:15; Deuteronomy 10:22.
To strengthen themselves in the strength of Pharaoh - To form an alliance with Pharaoh, that thus they might be able to repel the threatened invasion. Pharaoh was the general name of the kings of Egypt, in the same manner as Caesar was the common name of the emperors of Rome.
To trust in the shadow of Egypt - A ‘shadow’ (צל tsêl) is an emblem of protection and defense, as a shade is a protection from the burning rays of the sun (see the note at Isaiah 4:6).