First param in CActiveDataProvider could be a string with model name or instance of class. So, you may use CActiveRecord::cache() for cache, but you need set third param to 2, because you should cache 2 queries: counting and get data.
CFormatter is one of Yii's core components and used to format values displayed in widgets like CGridView or CDetailView. All classic formats like numbers, text, urls or datetime are supported but you may have to use a formatting rule that isn't built in. Let's say we want to display arrays of strings (like tags associated with a product model). When using CDetailView we would usually make use of PHPs implode function to create a simple string value of all values in the $product->tags array.
If you show a model (with a lot of attributes) partially in a CGridView, it can be helpful when the user can take a quick look at the full record with all attributes without displaying the view
as a page and afterwards returning back to the gridview.
There are situations in which Active Record will generate nonsense queries from what a nieve Yii user might think is reasonable code. One such situation is a CActiveDataProvider using CDbCriteria to get data from parent and 1:n child table with a condition on the child table.