Absolutely your business could be liable if the person is working for you at the time. Their insurance would be primary but you could be found secondarily liable. You can purchase a coverage called hired and non-owned coverage as an amendment to your business auto or liability insurance which would provide you coverage for this type of incident. The coverage is usually very inexpensive as it is secondary coverage.

It can be, but it just depends on the extent of coverage you purchase. Commercial Auto is not automatically included with Commercial General Liability.

If you purchase the Commercial Auto coverage along with the Commercial Liability then you will have the coverage. If you purchase only the commercial General Liability then you won't have coverage for commercial auto.

None, If you have a personal Auto Insurance Policy, " No coverage at all" will extend to you nor to any other injured party while you were engaged in a Delivery Service Business. A Personal Auto Insurance Policy is for the Personal use of your vehicle. Should you have an accident while engaged in a commercial enterprise, your personal Auto Policy will not cover the accident. While engaged in a Delivery Service Business with only a Personal Auto Insurance Policy in place, you are basically driving without coverage. Although a Business Auto Use Endorsement to your Personal Auto Policy will extend coverage for certain Business or job related errands such as occasionally picking up offices supplies and trips to meet with customers, Delivery services are always excluded from a personal Auto Policy. You need to obtain Business or commercial auto coverage to be compliant with your state Insurance Regulations.

What line of business (kind of coverage - Auto, GL...), please?

Commercial Auto Coverage is insurance that covers vehicles owned and operated for business use. A fleet of company cars, service trucks, etc.

Personal Auto Coverage is insurance that covers vehicles for individuals and families.