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
We can disable the inquiry form to the guest users by de-select the NOT LOGGED IN option under the Customer Groups. Reference guide: https://magediary.com/docs/product-inquiry-support.html#general-information
To enable the inquiry form only to the specific stores, select the stores that you want to enable in the Store View field under the General Information tab. Reference guide: https://magediary.com/docs/product-inquiry-support.html#general-information