Maybe I’m not understanding. Is the problem that your form is not showing at all or that you need to include the groups you want to display in the options. The reason why the field groups will not appear without specifying them is that your field groups location rule is to display on the “Post” post type and you are displaying the form on a “Page”.
Yes, you could have optional fields based on the taxonomy field. But the taxonomy field would need to be part of the same field group and the optional fields would need to be conditional fields based on the taxonomy field rather than making selections in the standard category meta box. It is not possible to display the standard taxonomy meta boxes on the front end of the site. This is a WP limitation, not and ACF limitation.
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