You can find input separately, and add a class to Active input in function rePosition() as,
$('#navigate tr td').find('input').removeClass('yourClassforText');
$('#navigate tr td').eq(active).find('input').addClass('yourClassforText');
// to select text inside input
$('#navigate tr td').eq(active).find('input').select();
old Demo Here
Update
As mentioned another problem by Op, is to remove only selected text.
You need to add a check on a keydown event as,
var inp = String.fromCharCode(event.keyCode);
if (!(/[a-zA-Z0-9-_ ]/.test(inp) || event.keyCode == 96)){
//if user is entering some text, neglect rePosition & reCalculate events
}
Updated Demo
Update - 2:
Demo with thead