1. Метод hasNegativeEvenNumbers(Stream<Integer>) возвращает true, если во входящем потоке есть хотя бы одно отрицательное четное число и false, если таких чисел нет. Для поиска чисел в потоке используй метод anyMatch() объекта типа Stream<Integer>. 
public static void main(String[] args) {
        String answerYes = "Yes";
        String answerNo = "No";

        Stream<Integer> stream1 = Stream.of(10, -22, 3, 12, -85, 0, 142);

        String answerNegativeEvenNumbers = hasNegativeEvenNumbers(stream1) ? answerYes : answerNo;
        System.out.println("Any negative even numbers in the stream? " + answerNegativeEvenNumbers);

        Stream<Integer> stream2 = Stream.of(10, 22, 3, 12, 85, 142);

        String answerOnlyPositiveNumbers = hasOnlyPositiveNumbers(stream2) ? answerYes : answerNo;
        System.out.println("Only positive numbers in the stream? " + answerOnlyPositiveNumbers);

        Stream<Integer> stream3 = Stream.of(-10, -22, -3, -12, -85, -142);

        String answerOnlyNegativeNumbers = hasOnlyNegativeNumbers(stream3) ? answerYes : answerNo;
        System.out.println("Only negative numbers in the stream? " + answerOnlyNegativeNumbers);
    }

    public static boolean hasNegativeEvenNumbers(Stream<Integer> stream) {
        return stream.filter(x->x%2==0).anyMatch(x->x<0);
    }

    public static boolean hasOnlyPositiveNumbers(Stream<Integer> stream) {
        return stream.allMatch(x->x>0);
    }

    public static boolean hasOnlyNegativeNumbers(Stream<Integer> stream) {
        return stream.noneMatch(x->x>0);
    }
}