How do I bulk close thousands of old tickets and send an automatic reply to customers at the same time?

There is no built-in way to mass close tickets and send a reply simultaneously. You can mass close from the Queue, but the reply must be done per-ticket. To close with a reply: open each ticket, add a Canned Response or paste your message, set the status below the reply box to 'Closed', then click Post Reply. This closes the ticket and sends the reply in one action.