4. Actuarial department is responsible for settling death claims
This is incorrect, "Actuarial department is responsible for settling death claims". Actuarial department is not responsible for settling death claims.
Actuarial department is responsible for analysing financial risks by implementing statistical, financial and mathematical theories.
They analyze the financial costs of risk and uncertainty and help businesses and clients develop policies that minimize the cost of that risk. They're expected to make a reasonable forecast of the future liabilities of policies.