Why is there unemployment even when the economy is at “full employment”?

1. Why is there unemployment even when the economy is at “full
employment”? What are some “costs of unemployment”?
2. Is the CPI a biased measure of the inflation rate? Explain your
answer.
3. Explain how some government tax revenue and spending can
depend on the state of the economy.
4. Explain some limitations of using GDP as an indicator of standard
of living (be sure to do some research on your own to find any
alternative measures).