They looked happy.是说他们看起来很高兴.happy 是形容词.
His dog always looks （happily） at him when he gets home from school every day.
也是对的.因为这里 这里 happily 是副词修饰 looks at ..看着.
他每天一回到家他的狗就很开心的看着他.
这里happily 也可以换些位置,比如.
His dog always looks at him happily when he gets home from school every day.