Does the government have the right to take a person's life who has committed murder? Why or why not?

I think the government does have the right to take away life. Government has the right to enforce laws that confine people to certain order. Consequences of deadly crimes should have equal punishment. If the consequences of breaking a law is the death penalty, and that consequence is stated before hand, then government has every right to act on the crime.
Murder should go both ways with a murderer. A person's life is precious, others may argue, but if that life is being used to kill other precious lives, then the government should be able to step in and do justice. Deadly crimes should have deadly consequences. The only way a person can draw the line if that murder was not intentional. That person deserves some sympathy along with punishment.
The death penalty doesn't make the institution more powerful, it just makes it more fair.

What is the nature of humans? Were we Created? Did we Evolve? Do we continue to exist after death? What is our ultimate destiny? Do we have a choice?

The nature of humans to strive for power and purpose. We are always in search of the reason we are on earth. We enjoying have power in the sense of possessions, a home, and friends. I believe we came through random events of evolution, but humans do have a purpose for being on this earth. I believe our souls do continue to live on after we pass. Our ultimate destiny is whatever God intends for it to be. We do have the free will to make the best out of our circumstances.