According to the group selected by the customer, could we show a specific set of fields on the ticket form?

For customers, we can show specific fields using Portal Customization. This can be done on the Estate & Forest plans. Please write to support@freshdesk.com with your requirements and we'll help you with this.

Another alternative is to have a dynamic form setup where you could add a section to the group's dropdown. Please follow this article to have this done at your end. Kindly note that this can be configured for any two custom dropdowns apart from the "Type" field.