Design patterns: extending jQuery objects with chaining + namespacing

I need help with JavaScript/jQuery design patterns. Below is some HTML and JS code illustrating what I do, and further below are questions extrapolated from these examples.

Some HTML with nested divs to create a traversing scenario:

    <div class="box">
        BOX 1
        <div class="nested-boxes">
            <div class="box">
                BOX 1-1
                <div class="nested-boxes">
                    <div class="box">
                        BOX 1-1-1
                    </div>
                </div>
            </div>
            <div class="box">
                BOX 1-2
            </div>
        </div>
    </div>

And here is the Javacript code:

// First I declare functions that I want to have available globally
// under a common namespace. Those functions reproduce that namespace as
// a prefix in their name to avoid conflict.
$.extend(true, window, {
    MyFunctions: {
        Boxes: {
            getBox: myfunctions_boxes_getBox
        },
        Circles: {
            // getCircle: myfunctions_circle_getCircle
        }
        // Squares....
    }
});

// I write functions which I want to use on jQuery objects as so:
function myfunctions_boxes_getNestedBoxes() {
    return this.find('.nested-boxes').first().children('.box');
}

function myfunctions_boxes_showLabel() {
    return this.find('span').first().text();   
}

// I then add those functions as new methods to my jQuery objects:
function myfunctions_boxes_getBox($element) {
    var $box = $element.closest('.box');
    $box.getParentBox = myfunctions_boxes_getParentBox;
    $box.getNestedBoxes = myfunctions_boxes_getNestedBoxes;
    $box.showLabel = myfunctions_boxes_showLabel;
    console.log('getBox',$box);
    return $box;
}

// Traversing functions call each other to make sure I retrieve a jQuery object with all
// my custom methods:
function myfunctions_boxes_getParentBox() {
    var $parent_box = myfunctions_boxes_getBox(this.closest('.box').parents('.box').first());
    console.log('getParentBox',$parent_box);
    return $parent_box;
}

Now this is what my code looks like:

// I first need to call a global function:
$box = MyFunctions.Boxes.getBox($('#box-1-1'));

// Then I can start chaining my methods
$box.getParentBox().getNestedBoxes().each(function(){
    // however as soon as I use a native jQuery method, I end up with
    // a jQuery object which doesn't have my custom methods ans I need
    // to use a global function again.
    console.log($(this), MyFunctions.Boxes.getBox($(this)).showLabel());
});

A jsFiddle showing this code in action (should it help you understand what I do) is available.

Q1: How can I write my functions without having to repeat the namespace as a prefix in their name (e.g. myfunctions_boxes_) while avoiding conflicts with third party code?

Every time I create a new function that I want to use as a custom method on a jQuery object (e.g. getParentBox, getNestedBoxes...) I have to manually map it inside one of my functions (i.e. myfunctions_boxes_getBox):

Q2: Is there a way to automatically map my custom methods?

The below question may be related to the above one but I prefer asking it separately as I feel they're not exactly the same

As soon as I use a native jQuery method (e.g. each in above example), I end up with jQuery objects which don't have my custom methods and I need to call one of my global functions again to retrieve the same object but with my custom methods attached to it.

Q3: Would it make sense to create a jQuery plugin for my global functions to keep the OO nature of me code (see below example)?

// plugin declaration (the getBox function should be modified to make use of this)
jQuery.fn.getBox = MyFunctions.Boxes.getBox
// then my code becomes cleaner:
$('#box-1-1').getBox().getParentBox().getNestedBoxes().each(function(){
   console.log($(this).getBox().showLabel());
});