Pressing Enter & Clicking the 'Next' button

Then in the “Edit JS Code” section of that plugin;
Select from the options in the right hand side;
– “External file”;
– “Footer”
– “In Frontend”

And add this code:

var $ = jQuery,
    context = $('#register-page'),
    submitButton = context.find('#signup_submit'),
    extraFields = context.find('#extra-fields'),
    extraFieldsTrigger = context.find('#show_extra_fields');

// If the additional fields are hidden
if (extraFields.is(':hidden')) {
    // Disable the submit button
    submitButton.attr('disabled', 'disabled');
}

// If the Next button has been pressed
extraFieldsTrigger.on('click', function() {
    // Enable the submit button
    submitButton.removeAttr('disabled');
});

See https://wordpress.org/plugins/custom-css-js/screenshots/

Unfortunately that’s not allowed. Take your time, I won’t disappear.

Yes that’s right

Nothing other than making sure the options on the right-hand side are set as:
– “External file”;
– “Footer”
– “In Frontend”