HP Deskjet 2542 Wireless AIO Printer

What model HP Print Cartridges does this take?

Can i print from my smartphone

Sure can! I have a similar model; when you set things up, you’ll get an email address to the printer that you can sent pics/docs from your phone to the printer.

Am I able also to fax with this ?

Looked through the manual on the HP support page and I don’t see any reference to FAXing.