Tutorial-First-Application VS Aura.Payload

b) Separate out all SQL and PHP database code. Put these in separate classes similar to this example Slim First Application Mapper class. You can decide later if you want to use a framework's DB code or not - it would be simply refactoring your existing code and not changing (hopefully) the API that you started using internally

Yes, as an example, the First Application's business logic (not that it's much) doesn't tie itself to the framework, as one example. Odan's Slim Skeleton, ADR Example (yes, I know you are the author), and the Aura Payload example class can be seen as other examples.

Both. Build business logic with PHP, then use a framework for the common functionality (routing, auth, validation, etc). Look at Slim's First Application to show a very simple example of this - https://github.com/slimphp/Tutorial-First-Application

Another option, to me and speaking to the OP as an alternative, it is simpler to add some Data Mappers/Repositories to abstract away the Database code. Good examples is the sample ADR application, Payload library example, Slim 3 First Application, or this Slim 4 Skeleton application

Yes, you can. Did you look at the example I provided? Want another one? Slim Framework's first application does exactly this:

https://github.com/slimphp/Tutorial-First-Application <- Uses the Slim framework

https://github.com/auraphp/Aura.Payload/blob/3.x/docs/index.md - Service CRUD class example in the docs.