Should APY and Rate be exactly the same, since APY assumes funds on deposit for one year and no withdrawals of interest? Is Simple Interest method is calculated the same way?

Simple interest would have the same rate and APY. If the interest is compounded (daily, monthly, constantly, etc.) the APY would be higher. And always keep in mind that the APY means annual percentage yield.

Here is one APY calculator out on the net.

Do take note of whether the account in question is a time account (certificate of deposit) for less than one year. For these accounts, even if they pay simple interest, the APY will be greater than the interest rate. That's because the rules require the bank to assume that the deposit and interest remain on deposit for one year. If the CD is written for 6 months, the interest is assumed to be capitalized (compounded) at the first maturity.