Moving out of Auth0
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 are the password hashes of your Auth0-hosted database users and private keys, for security reasons. You can still request this information by opening a support ticket. Please note that this operation is not available for our Free subscription tier.
Keeping user credentials on your infrastructure
If you want to store user passwords on your database, you can 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.
I don't want to use proprietary Auth0 components
Auth0 mainly 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 applies when integrating Auth0 through SAML.
All of Auth0's SDKs, libraries and samples are published on GitHub as free software.
If you choose not to use Auth0 but 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 Webtask, which is a Node.js sandbox service. In the vast majority of cases, Webtask code is also valid Node.js code or can be adapted with minimal effort. All libraries available on Webtask are also available on npm for use with standard Node.js code.