It's a bit more complicated than that. You have a period of time to delete the data. And you can keep enough info to know what data you've deleted, so that if you restore from backups you are able to re-delete without having to go through your backups and delete everything. Probably more that I'm forgetting.

You can keep contact info even after a GDPR deletion request, so long as you're not using it for business purposes.

Otherwise imagine how easy it would be to violate the deletion request if you're running a business and can't remember the names of the people you had deletion requests for. Their data could come up again through normal channels and you'd treat them no differently than another sales contact, thus violating GDPR.

Depends on type of data and other laws. If you are a paying customer you can assume your data will be stay in database, until it is no longer required for audits. GDPR allows for anything that is 'absolutely totally required for providing service'.