I have also invested in FDs with my Savings account, what would happen if I becomes NRI?

As a resident, if you have invested in FDs linked to your bank savings account then while converting savings account to an NRO account, you have to attach FD receipts with the documents. You can re-designate FD investment as a resident to NRO FDs. Interest earned on NRO FDs will be subject to 30% TDS.