Custom fields can be applied to taxonomies themselves, but I'd like to confirm if it's possible to assign a group of fields to posts under a certain taxonomy only?
Solution:
You can try these:
Edit the post field group you mentioned above, in section "Settings for YOUR FIELD GROUP", just after "Appears on", click button "Edit", here you can choose specific taxonomy term
On the edit field group screen when creating or editing a field group the button doesn't appear for adding a field group.
Solution:
The repeatable field groups are based on new Toolset post type relationships, but your website is still using the legacy post type relationship, so the button "Add New Group" isn't available in your website.
Please try these:
1) Backup your website, especially database.
2) Dashboard-> Toolset-> Relationships, click "Run the migration" button, then test again.