Hi,
Let me try to address some of your questions, as I'm helping a client build out an internal developer portal for their future API platform:
1. Registration isn't necessary to review the docs - in fact, I encourage low friction for those learning about the API. Registration should only be required once they wish to consume the API, via HTTP using cURL/Postman/etc, using code, or from interactive reference docs
2. The developer portal won't handle the API requests itself, you need to stand up an instance of the API or point it at production. The easiest option is to have a single developer portal that offers currently available APIs and points to a sandbox for interactive documentation, as that allows for experimentation without impacting production. The sandbox can have a subset of data from production, perhaps cleansed to remove PII and other sensitive information, or it may be a set of known working data for exercising known scenarios that mimic production. You can get a little more robust if needed by adding in a developer portal per environment, e.g. production and staging, allowing your documentation to point to that specific environment's APIs and reflect what is currently available in those environments. You'll need to script that promotion logic alongside your code promotion process in your CI/CD automation.
3. I suggest code snippets to exist outside of Swagger, as Swagger (et al) is really for capturing API definitions that can drive reference documentation. The developer portal should offer a high-level view of the domain concepts offered by the API, to help those new to the company or to consuming the API. You can also offer code examples at the same time. Some APIs, such as Stripe, offer examples in various languages alongside the reference documentation, which is helpful for understanding the specific endpoint but aren't always complete enough to demonstrate end-to-end use cases when complex workflows are involved. You need to determine what is necessary to support your target audience, mixing in reference documentation with anything else you need to help API consumers to be successful. You may also want to consider the needs of those outside of development, such as product owners and business leaders that may wish to understand the API's capabilities at a higher level.
James