I have been to Iceland recently and tap water is absolutely fine to drink directly and preferred. No one there buys water. Just make sure you drink the cold water and not the hot one as the hot is from natural thermal springs so may contain some minerals I belive. Just carry your own bottles and you can fill up the cold water from anywhere, even restaurants will refill free.
K9 mail on Android since many years and Thunderbird on laptop, also since many years. Also use Gmail, Yahoo Mail.