Yes, it is possible to implement the functionality you described for exporting user data to their own site and maintaining a list of requests on the administrative side for traceability purposes. This can typically be achieved through the development of custom features or by integrating existing tools and plugins that provide such functionalities.

For exporting user data, you can create an interface or tool on your website where users can request their data to be exported. On the administrative side, you would have a system to manage these requests and process them accordingly. This may involve verifying the identity of the user making the request and exporting the relevant data securely.

Regarding the integration of cookies and GDPR compliance, it is indeed possible to customize cookie components on the administrative side and integrate them with GDPR compliance tools. This can include tracking user consent for various types of cookies, providing options for users to manage their cookie preferences, and ensuring that consents expire or are renewed as required by GDPR regulations.

It's important to note that implementing such features requires careful planning and consideration of data privacy and security principles. You may need to consult with legal experts or GDPR compliance specialists to ensure that your implementation aligns with regulatory requirements and best practices. Additionally, thorough testing and ongoing monitoring may be necessary to maintain compliance over time.