Question about GDP, Macroeconomics

Relevant Reading:

guide on price indexes provided by the U.S. Bureau of Economic Analysis:

https://www.bea.gov/resources/learning-center/quick-guide-some-popular-bea-price-indexes

a) What is the practical advantage of using the PCE Core price index relative to the PCE price index?

b) Does this practical advantage matter more for month-to-month inflation rates or month-to-same-month

one year before:

c) Why does the GDP price deflator exclude the price of goods and services imported in the U.S but includes the prices of goods and services exported by the U.S.?

d) Why does the GDP price deflator exclude the price of imported goods and services while the PCE price index includes the price of imported goods and service?

e) Which price index measures the price index of U.S. absorption?