Which balance-of-payments account would a country refer to in order to understand the value of all the merchandise and services plus unilateral transfers of funds that have been imported and exported?

The country would refer to the balance of payments current account.

Explanation:

The balance of payments current account is the account which measures all the exports, imports and unilateral transfers of funds, so all the services and goods being sold by the country to other countries, and bought by the country from other countries is recorded on the current account of balance of payments.