Answer:
1. Charles's employer assigns him to provide consulting services to an Australian firm that's opening a manufacturing facility in China. - exports (X),
Exports include the goods or services that originate in the US and are then sold to entities outside the USA. Charles works in the US and is providing services to an Australian firm so this qualifies as an export.
2. Dina buys a new BMW, which was assembled in Germany. - Consumption and Imports
Consumption refers to amounts spent by households or people in the Economy on goods and services. Imports refer to the use of goods and/ or services that did not originate in the US. Dina both spent on a good as well as the good being from outside the US making it both Consumption and Imports.
3. Gilberto buys a new set of tools to use in his plumbing business. - Consumption.
Consumption refers to amounts spent by households or people in the Economy on goods and services so Gilberto spending on a new set of tools qualifies as Consumption.
4. Dina gets a haircut. - Consumption.
Consumption refers to amounts spent by households or people in the Economy on goods and services so Dina getting a haircut which is a service falls under Consumption.
5. The Federal Aviation Administration expands the runways at Philadelphia International Airport, which is just a few miles from Charles and Dina's house. - Government Purchases
Government Purchase which are otherwise known as Government Spending refer to money spent by the government in an Economy. The FAA is a Federal Government agency so expanding the runway is a Government Purchase.