1. There is a chance that some of Alice and Bob's children will have brown eyes, since both Alice and Bob are brown - eyed. However, there is no chance that a child of them will look like Bob's father, so this means that no child of Alice and Bob can have brown hair. As Alice has blond hair herself, it means that Bob also must have blond hair (else he would have a dominant allele for brown hair, which could be transferred to produce an auburn offspring). Therefore, Bob is blond.
2. Bob has blond hair and brown eyes, but his mother was green - eyed, so he must have inherited a recessive green - eye allele from her.
So, if we denote by H the (dominant) allele for brown hair, by h the (recessive) allele for blond hair, by E the (dominant) allele for brown eyes and by e the (recessive) allele for green eyes, we conclude the following.
Bob's genotype is hhEe (because he has blond hair, and brown eyes, but has inherited an allele for green eyes from his mother).
Alice knows for sure that her daughter will be blond. So, the fact that Alice knows there is a small chance her daughter might look like her mother is only related to her daughter's eyes. And since there is only a small chance that the daughter will have her grandmother's eyes means that the grandmother had green eyes, and so Alice also has genotype hhEe. So, she definitely inherited the brown eyes allele from her father.
Therefore, Alice's father has brown eyes, and Alice's mother has green eyes.
3. Since both Alice and Bob have genotype hhEe, they can have a blond son with green eyes with probability $\frac{1}{8}$ (since there is a probability of $\frac{1}{4}$ of having a child with green eyes, and a probability of $\frac{1}{2}$ of the child actually being a boy.
4. Since both Alice and Bob are blond, they can never have auburn children, since they don't have the required allele. So the probability of them having an auburn daughter is zero.