If your instance is hosted by Adobe, ask support to install GPG utility on the server.
Get public-private key pair generated for outbound transfer.
While doing export, you can encrypt the file on Campaign server and also provide the public key to external sFTP server team for decrypting the file. And use vice-versa to decrypt the file to decrypt at adobe campaign.
This can be done in file load activity and js activity, and for all the transfer via the database, it happens via secure transfer so that should be covered.
For deletion, if it's hosted by Adobe you are covered because it's Adobe's responsibility to ensure the compliance if it's on the premise, Move all the data marked as delete to an Archiving location and use Gutmann method to delete which will ensure that you are covered.
Can you confirm that your requests are related to GDPR compliance?
In any case, I'd recommend reaching out to support so they log in all your different requests and provide you with the existing solutions, and put you in relation with our security specialists directly, since people on this forum won't have real insight on GDPR enhancements before it's live in a few months.
Encryption and anonymization are I think already possible with Campaign. As for the other parts, some product enhancements are on the way to help companies using Adobe products to comply with GDPR regulations. More information will be provided shortly by the product team (in a few weeks).