phroute VS Tutorial-First-Application

The router code for this could look like (using Phroute for the example). The functions could be sent to classes if you have that setup.

Finally, add a router to map all of this out. You could use a library, some one noted FastRoute, there a few out there like Phroute for one.

How hard did you look? There are plenty out there. FastRoute, Phroute, based on FastRoute, with basic middleware, League/Route - routing with middleware, using FastRoute, PSR 7 & 15, Slim Framework, at it's core, it like League/Route, etc. None of these require a full framework to use.

Using a router library like FastRoute or Phroute to show the example

Someone mentioned FastRoute. You can look at Phroute as well - https://github.com/mrjgreen/phroute

Additionally, you lose the checks at the top of those files (here' and here if you implement middleware. Here is one example using pretty URLs and a router library. Using Phroute to show the example - pseudo code to illustrate:

Using Phroute to show the example

This can be refactored. If you use start using a router and middleware, this can be done as middleware (or a before/after filter for older libraries - See the Filter Group section on this library for example usage - https://github.com/mrjgreen/phroute)

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