Can science answer moral questions?
Yes and no. Moral questions are partially based on knowledge of facts, which can be discovered through scientific observation, reasoning, and experimentation. However, all moral questions depend on one decision: what is most important? At the most fundamental level, science can't tell us whether preventing suffering, spreading knowledge, or forming relationships are more important than each other or any other fundamental value.
Once you've chosen what is most important to you, then science is one important way to decide how to reach that goal. If close relationships are the most important to you, then you can become a social scientist and study which relationships are the closest, how to encourage them, etc. Science can focus your values: you may find that marriage influences happiness more than any other relationship, and since you value happiness, you go into marriage counseling.
It is my belief that God is the source of all good values. He gives us a conscience so that we will be able to choose values that are consistent with His. The more consistent our chosen values are with His, the better our existence will be after death, in every conceivable way.
As a Christian, I believe that Jesus Christ exemplified the two most important values: love for God (which includes love for goodness in every form, since God embodies all good values), and love for fellow humans (which includes honesty, compassion, etc.). In Jesus, these two values formed an unbreakable foundation for all other, lesser values.