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
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
Yes, set the Enable for Product View and Enable for List View fields accordingly under the Permissions tab. Reference guide: https://magediary.com/docs/product-inquiry-support.html#permissions