Unable to Alter Model Data Using Ember API Kit

Question 1

It seems like you're coming from a jQuery background because of how you're trying to embed the id of your ClassGroup records into the DOM via the template (nothing wrong with that of course as that's what I was doing when I first started with Ember coming from a jQuery heavy background). If you notice yourself doing this you're probably doing something in a non-ember way. Generally, you should only be accessing DOM elements by ID if you need to integrate some 3rd party jQuery library.

Okay, so now you know what to look out for how should we accomplish what you want in the Ember way?

There are probably several ways to go about it but what works well for me is to create another controller for each individual ClassGroup that extends ObjectController instead of ArrayController. So you would have

ClassGroupsController (ArrayController) -> ClassGroupController (ObjectController)

Notice that the array controller is pluralized. What this allows you to do is to manage the state of each individual ClassGroup record because each ClassGroup record now has its own controller and its own view.

So First create an array controller that manages the collection of ClassGroups:

App.ClassGroupsController = Ember.ArrayController.extend({

});

The ClassGroupController (Object) should then have a view which listens for click events. When we get a click event we trigger an action on the controller (ClassGroupController) called selected.

App.ClassGroupView = Ember.View.extend({
    templateName: 'classGroup',
    /*
    By specifying the tagName for this view we are telling ember
    we want to wrap the view in a <tr> element.  This is because
    each classGroup is going to be a row in our table.  By default
    each view is wrapped in a <div>
    */    
    tagName: 'tr',
    /*
    This is the click handler that is called whenever the user
    clicks on this view (in this case one of our <tr> elements
    that is displaying our ClassGroup Model for us.  The event
    parameter is the jQuery event object.
    */
    click: function(event){
        /*
        We want to forward this event to the controller where
        we can do some logic based on the fact that it was clicked.        
        */
        this.get('controller').send('selected');   
    }
});

Now we create our ObjectController for ClassGroup which is waiting and listening for the selected action which is being sent from the ClassGroupView when the user clicks on that individual ClassGroup.

App.ClassGroupController = Ember.ObjectController.extend({    
    actions:{
        /*
        This is the action we received from our view which was
        based on the user clicking on one of the <li> elements
        representing a ClassGroup Model
        */
        selected: function(){            
            console.info("You selected: " + this.get('className'));    
            /*
            Now we can easily toggle the isActive state of our model
            */
            this.toggleProperty('isActive');
            console.info("My isActive state is now: " + this.get('isActive'));
        }
    }
});

Now we need to connect this up in our template.

{{#each itemController="classGroup"}}
    {{view App.ClassGroupView}}  
{{/each}}

Notice how I specify that I want to use the classGroup as an itemController for my ArrayController. Here I specify it directly in the template. You can also specify it in the ArrayController itself using the itemController property. So for example:

App.ClassGroupsController = Ember.ArrayController.extend({
    itemController: 'classGroup'   
});

Here is a working JSFIddle using your fixtures to demonstrate the entire concept:

http://jsfiddle.net/NQKvy/872/

Question 2

To directly answer your question

you can find a record by id and modify it using

this.store.find('classgroup', id).then(function (classgroup) {
    classgroup.toggleProperty('isActive');
});

However in your case you don't really need to since you can just pass the record

so in your view use

{{action "isActiveTog" this on="click"}}

instead of this.id and then just directly modify it in the controller

isActiveTog: function(classgroup){
    classgroup.toggleProperty('isActive');
    // classgroup.save();
}