When we say 'Savings Account', does it automatically mean that the interest rate can go up and down? So by that definition, the interest rate on TFSA can go up and down any time?
TFSA is a misnomer. It is not a Savings Account, but a registered Savings Plan. For example, My TFSA is in mutual funds, so there is no interest as such. I make my earnings through share value growth, and dividends. If you want a guaranteed return, then you put it in GICs.
You can put TFSA funds in a savings account (which is essentially keeping it in cash), in which case the rate would fluctuate just like your regular savings account.
However, I believe the best strategy is RRSPs should be stable and secure, and TFSA's should be higher risk/higher reward, giving you the tax free benefit on the bulk of your earnings.
In general, when we say savings account, yes the interest can go up or down at anytime. Some savings accounts link it to the Prime Rate explicitly, others change the interest paid every now and then, usually in response to changes in Prime Rate.
When you say TFSA, as chris alluded to, you must be talking about a TFSA savings account. The interest rate on that account then varies in the exact same way as a non-TFSA savings account.