Is water a nucleophile?
Yes, water is a nucleophile.
Water is both a nucleophile and an electrophile.
It acts as nucleophile by sharing a pair of electrons with an electrophile
H₂O: + E⁺ → H₂O⁺-E
and as electrophile by giving a proton to a nucleophile.
Nu: + H-OH → Nu⁺-H + OH⁻