Dear Sir,
1) File ITR as legal heir of your grandmother atleast for two Assessment years (2017-18 and 2018-19). In all these 10 years, TDS was deducted and no return was filed. Now you need to obtain permission from the department to file ITR of previous years because TDS was deducted and no one claim the credit of such TDS amount. If you want to claim it the you need to meet her jurisdictional AO. Check if any notices have been received for non-filing of ITR of your grandmother. No need to show this deposit in your ITR as FD amount is capital receipt in your hands. Only interest will be taxable in your hands as per the slab rate.
2) If you have submitted yours PAN details in bank then bank will deduct TDS on your PAN for which you needs to file ITR (for FD interest) each year. You need to file ITR on yearly basis and not only at the time of maturity of FD because FD interest is chargeable to tax on accrual basis and not on receipt basis.
3) Yes you can open FD on your single name after receiving the maturity amount.
4) ITO will ask from you only about the source of FD in your hands.
5) To file ITR of your grandmother you need to obtain legal heir certificate.
Thanks