All data in your Auth0 tenant is always under your control and is available through the Management API at any time.
The only information which is not available through the API (for security reasons) are the password hashes of your Auth0-hosted database users and private keys. You can still request this information by opening a support ticket. This operation is not available for our Free subscription tier, and we are unable to accept or guarantee requests for exports at a specific time and date.
If you store user passwords in your database, set up a custom database connection which Auth0 will query each time a user logs in. In this case, Auth0 will never store any password hashes, unless you choose to progressively migrate users to Auth0.
Auth0 primarily uses OpenID Connect (OIDC) as its authentication protocol, so you should be able to implement an integration to your application using standard libraries. The same situation applies when integrating Auth0 through SAML. All of Auth0's SDKs, libraries, and samples are published on GitHub as free software.
Social identity providers
If you choose not to use Auth0 but want to keep using the same OAuth client IDs and secrets for your social identity providers, you will retain access to user information without needing to display new consent dialogs.
All of Auth0's custom code features (rules, custom database scripts, custom OAuth connections, and so on) run on a Node.js sandbox service. All libraries available on the sandbox service are also available on npm for use with standard Node.js code.