I can also confirm that printing is possible without a printer. You just have to connect the mobile phone or tablet to the printer and print via AirPrint. So far I have had no problems with Android and iOS.

The printer must receive the data from somewhere. If you don't have a router, then you have to make a WLAN (mobile hotspot) access point with the IPhone and then register the printer in this network. It doesn't work with the iPad.
This has nothing to do with the Epson printer, it applies to all printers.