Contact form inside popup?

The plugin simply opens the target of your link in a new browser window.

If you can create a page your site to contain your form, set it up with a landing-page type template, make that page the link target for the popup, and also trigger some javascript on the form’s submit button to close the window once the form is submitted, then you will be able to use this plugin as part of the solution to achieve what you have described.

This functionality is not core to the plugin so you will need to set up other elements (forms plugin, landing page template etc) as described to build it to work as described. Consequently it is beyond the scope of the free support I can provide for this plugin.

Not related to this, but you may want to reconsider the name you have chosen for your site: https://en.wikipedia.org/wiki/Heaven%27s_Gate_%28religious_group%29