Setting cookies is fine. If they are needed.

You need a session cookie for the login function the user uses? - Use a cookie. No banner needed.

The user puts something in their shopping basket? - Use a session cookie. No banner needed.

You want to store information, not required, in order to identify the user again even though they didn't login, maybe to share the identity with an ad network? - You need a cookie banner where the user can opt out easily.

Not only that, but storing information to identify the user again requires affirmative consent. GDPR doesn't just require that the user can opt out of tracking, but that any tracking occurs only after the user has freely given informed consent.

Yes. If your users create an account with name and address data they need to agree to that data storage.

If your shop just sells them a virtual thing there is no need to collect personal information.

If you ask for the address and more or less directly print it on the label and then delete again it is a bit of an edge case where no explicit confirmation might be needed, however having a good data policy is good practice anyways and then having the extra checkbox in the order flow is not a big deal.