No. Vivo S1 does not have Qualcomm Snapdragon processor but it has latest the latest MediaTek P65 octa-core processor.
Yes, Vivo S1 does have a 3.5mm headphone jack.
No. Vivo S1 does not have the FM radio support.
Yes, Vivo India does provide a complimentary protective case inside the Vivo S1 standard packaging.