Is the KISS Principle More Important Than Utilizing OOP?

First, I think you're asking many questions, not one.

And half of the answers of these questions is the ever correct "It depends".

In general, exposing object ivars directly is discouraged if you're aiming for looser coupling (obviously). Although I think when it comes to IBOutlets it is an acceptable practice, since after all the Interface Builder is tasked with the creation of the object.

On the other hand, a readwrite property for an NSInteger makes little sense, unless you're doing something very funky, and you can easily use an ivar instead.

Once upon a time, in pre-ARC ages, there were some people, who advocated always using properties for objects, since then you don't need to care about retain/release. However now that ARC is widely used, this makes almost no difference and it is mostly a cosmetical thing.

A final piece of advice: aim for consistency project-wide.

EDIT: I'm not the greatest fan imaginable of Design Patterns, but it seems that most of your questions would find the best answer in this book.

Your title does not seem to mach your question, and your question has little to do with reporting, so that might explain why you couldn't find much.

Your problem start to emerge here:

I have designed all the three classes to include all the operational logic (details of which are not relevant in context of the question).

I don't think you should put "operational logic" (do you mean data access operations like get, update and delete?) in your model classes.

for example, say, a list of all students doing projects in Chemistry mentored by a teacher whose name is the parameter to the query.

To me, it sounds like you're looking for the repository pattern. Something like:

class StudentRepository
{
    private $_database;

    function GetStudentByID($id)
    {
        return $_database..[query with $id];
    }

    function GetStudentsForSubjectAndTeacher($subjectID, $teacherID)
    {
        return $_database..[query with $subjectID, $teacherID];
    }
}

Now everywhere you want to find all students for a given subject and teacher, you just create an instance of this repository and call the appropriate method.