Is the billing date of credit card the same as transaction date? How do I know when is a new cycle?

You can look at your previous month bill. Statement date is the last day of the billing cycle. The next day after statement date is the first day of new billing cycle.

Do note that for some merchants, it may take a day or two for the transaction to be posted. If the transaction is posted after the statement date, it will be counted as the new billing cycle.

Another date to take note of is the Payment Due Date which is generally around 20 calendar days from the statement date (depending on the banks), after which, late fees and finance/interest charges may incur.