What about using this feature without obliging a customer to create an account (just provide us your first & last name and your email, pay, and we'll display you download links (+ mail including these links). Does this represent much work ?
This is configurable out of the box. No custom code required.
Is it possible to setup or develop such a service (which would for exemple return a download links list when requested for a customer email). Does the Sitefinity API provide such posibilities ?
Yes. But for a web service based (access from another site) you may need to implement your own custom service that wraps the API. The current services are limited to querying, deleting, and modifying sitefinity ecommerce items.
I hope this helps.