I want to select my seats but I'm directly being sent to the payment page.

If you were redirected to the payment page without being able to select the seats or without being shown the seat layout, chances are that the event that you're looking for is a standing event or is a free seated event that would function on a first-come-first-serve basis. This varies from event to event.

I've booked my seats, but why does the confirmation not have a seat number?

If you've already transacted and don't remember selecting seats, you can always refer to your confirmation. If they still lack specific seat numbers, it's a free-seated or standing event.