How can i make a website connect directly to a printer? so that it can print out the orders directly

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Pre-requisite is that you have a way to let the webserver talk to the printer. This is the case if the printer is attached to the webserver, the printer is on the same network as the webserver or the webserver has a VPN link to the printer's network. If any of that is the case, then you can collect the data from the shopping cart on submit and print out the order form using for example IPP as AJ pointed out. There is no need to use periodic prints. Printers have their own spools and you may as well print the order at the time that it is valid.

If you do not have a way to communicate with the printer, then it's a whole new ballgame. I would send an email (using PHP's mail() function or any of the mailer packages out there) to a special email address which calls a program that strips the email headers and does any needed formatting. In that case, the printer needs to be on the same network as the email server. To answer this properly, we'd need more info about the mailserver environment.