jQuery to serialize only elements within a div

No problem. Just use the following. This will behave exactly like serializing a form but using a div's content instead.

$('#divId :input').serialize();

Check https://jsbin.com/xabureladi/1 for a demonstration (https://jsbin.com/xabureladi/1/edit for the code)

You can improve the speed of your code if you restrict the items jQuery will look at.

Use the selector :input instead of * to achieve it.

$('#divId :input').serialize()

This will make your code faster because the list of items is shorter.

serialize all the form-elements within a div.

You could do that by targeting the div #target-div-id inside your form using :

$('#target-div-id').find('select, textarea, input').serialize();