The Account Group object is used to tie an Account to a Price List. This allows you to assign different Price Lists to different groups of Accounts. For example, you could have one Price List for wholesale customers and another Price List for retail customers.
Reference:
Salesforce B2B Commerce Administrator Trailhead module: https://trailhead.salesforce.com/content/learn/modules/b2b-commerce-basics

One possible reason for the custom fields in the Order Summary to be empty in the export file is that the developer does not have access to the fields. Data Loader respects the sharing and security settings of Salesforce objects and fields. Therefore, if the developer does not have access to view or edit the custom fields in the Cart and Order Summary objects based on their profile or role permissions, the fields will not be included in the export file. The other options are not likely causes because:
A misspelling in one of the custom fields would not affect the mapping from Cart to Order Summary or the export of Order Summary data. It would only affect the display of the field label or API name.
The Cart to Order action does support the mapping of custom fields as long as certain patterns are followed. To be automatically mapped, the custom field needs to exist in the Cart, Order and OrderSummary objects and have the same API name, supported data type and field configuration1.
The developer can export Order Summary records by using Data Loader or Data Export Service. Data Loader is a client application that can export data for one or more standard or custom objects. Data Export Service is a web-based tool that can export data for all objects in an org on a weekly or monthly basis.

General coupons allow you to create complex coupon rules with AND/OR conditions. This means that you can create coupons that apply to customers who meet multiple criteria, such as purchasing a specific product and spending a certain amount of money.
Reference:
Salesforce B2B Commerce Administrator Trailhead module: https://trailhead.salesforce.com/content/learn/modules/b2b-commerce-basics

Explanation
The first price Tier is defined on the Price field on the respective Pricelist Item Record. This is the price that will be displayed to users on the storefront.
When using Tiered Pricing, the first price tier is defined in the Price field on the respective Pricelist Item Record. Each Pricelist Item Record represents a specific product and defines the price tiers associated with that product. The Price field on the Pricelist Item Record determines the price for the first tier of the product.
References: Salesforce B2B Commerce Administrator documents or study guide (specifically, the section related to Tiered Pricing and Pricelist Item Records).