My inference from your question is that this is a low profile project, and you have enough flexibility from your boss/client/teacher that you can build it however you want. That in mind, here is what I would think about when working on this.
If MVC is a new concept to you, then Test-Driven Development is almost certainly and alien one as well. However, I first cracked into a real understanding of OOP while doing it, so I suggest you give it a try. Writing some simple unit tests first against your model classes will take you through the exercise of figuring out how those model classes are going to be used. You'll be working with the external API of each of those objects (or groups of objects if you're not a TDD purist), and that will help guide the design of the internals. Check out PHPUnit for getting started, as the documentation has some great examples as well.
I think the TDD approach will lead you to the following conclusions:
- Probably not. Static data/methods are usually only useful when you absolutely need one copy of something. I find in web apps that aside from maybe a resource connection like the DB this is rarely the case.
- This depends on what the function does. Keep in mind that using local variables implies side-effects, or changes in the state of the object. If the data you need to operate on should not change the state of the entire object, use a parameter and return a value. It's also easier to test these kinds of methods.
- Again, writing tests for these functions that illustrate how you'll use them in the application will lead you to a conclusion one way or another about whether you need them or whether they are designed correctly. Don't be afraid to change them.
- Absolutely. How else are you going to become comfortable with MVC if you don't roll your own implementation at least once? In fact, it's probably better to grasp the concepts with real experience before you move to a more professional framework. That way, you'll understand why the concepts and conventions of the framework are the way they are.
Oh, and the lack of clarity that you're finding on what a model class is, is probably due to the fact that it's the part of your application that is most customized. This is your data model and domain logic, so a lot of it is case-specific. The best resource, though, IMHO is Martin Fowler, whose excellent book Patterns of Enterprise Application Architecture goes into a lot of detail on how and why to design a particular set of "model" classes with one pattern or another. Here is the online pattern library--obviously the book is more detailed.
Hope that helps somewhat.