Find element that's on the middle of the visible screen (viewport), on scroll

Answer 1

The height of the window and the scrollTop() of the window will give you the range of offsets that exist in the users view:

var minHeight = $(window).scrollTop()
var maxHeight = $(window).height()
var middleHeight = (maxHeight + minHeight) / 2;

You could try using a viewport selector such as: http://www.appelsiini.net/projects/viewport This will give you all visible elements. A plugin isn't needed but will ease the selection

var visibleElements = $("div.box").filter(":in-viewport")

From this selection you can then look for the element closest to the middleHeight:

var $midElement;
var distance = null;
var currDistance = 0;
visibleElements.each(function(index, element) {
    currDistance = Math.abs(middleHeight - $midElement.offset().top);
    if ( distance == null || currDistance < distance ) {
        $midElement = $(element);
        distance = currDistance;
    }
});

Haven't tested this but it should be along the right track.