Yes, the admin can set the conditions like show the inquiry form only for products which attribute set is Bag or category is Gear. Reference guide: https://magediary.com/docs/product-inquiry-support.html#conditions
If a product has multiple labels then it shows all the labels until the Discard subsequent labels option set to Yes for a rule. Reference guide: https://magediary.com/docs/product-labels.html#label-information
Yes, to show the selected simple product's label set the Use for Parent to Yes under the Label Information tab. Reference guide: https://magediary.com/docs/product-labels.html#label-information