can i ask a noob question - must you always have a savings account with a bank before you open an FD account with them?

Lets say i have a MBB account and since the rate is crappy - i want to put FD in UOB.. must I first open a UOB savings acc? if so, what happens after the 1 year that i place the FD - my UOB acc just remains or can i opt to close it?

If I got e-FD in Maybank on a monthly auto renewal, will the new rates apply at the next renewal or would the old rate still apply? currently it is 3.0%.

thnx