2. Can I do it only if they consented to receive marketing emails from me or maybe to customer who have an account with the store but not necessarily subscribed to marketing emails?
1.No you cannot send marketing e-mail to a customer that didn’t finish his order because consent is needed for direct marketing unless you send out marketing ma terials to existing customers (see the answer to your question number 3). In order to be valid the consent from a customer must be freely given, specific, informed and unambiguous indication of the individual’s wishes (https://advisera.com/eugdpracademy/gdpr/conditions-for-consent/ ). The principle of “opt-in” is a must, meaning no processing can take place until consent is assured. A data controller is required to be able to demonstrate that consent was given. Not finishing the order means that his consent is ambiguous and doesn’t represent a clear indication of individual’s wishes. You can however send a reminder that the customer did not finish his/her order.
2.Yes, you can send to your customers direct marketing e-mails ONLY if they consented. For the customers who have only an store account but they haven’t subscribed for marketing e-mails you cannot send them marketing e-mails.
3. You are required to get consent only for new customers, for the existing customers you can rely on legitimate interest to carry out your marketing activities. For prospects and leads you may need to obtain their consent if you want to send them marketing materials. You can continue sending marketing emails to your existing clients based on legitimate interest proved you leave them the choice to refuse marketing (opt out) as for prospects most likely you need their consent. So, unless you have appropriate grounds for processing personal data for marketing purposes you should not sent marketing.