Seeking a Better way to Create a Collapsible Fieldset
Form submit would not work unless you have an action for it. 

You should rather do it in Drupal way, you will need following.


Create Custom Module in drupal.
Block API to create your custom block
Forms API. to create a custom form and call it in your custom block.


Here goes a demo module which will help you understanding the API
https://github.com/arpitr/demo_block_form

Installing the module will give you a block which will look like as