Heard that iPhone and peripheral accessories can be combined into a new item, want to know is the printer can connect with the iPhone..

You can install AirPrint on your iPhone which will allow you to print to any Airphone enabled printer. HP has full line of Airprint enabled printers.

"There are three basic types of iPad printing apps. The first, supposedly, print directly to Wi-Fi-enabled printers. The second look out on your Wi-Fi network for Macs sharing printers, and can print to the shared printers without any intervention from the Mac's user. This is a decent solution if you go somewhere with Macs and printers. The third type requires you to run a server in the background on a Mac or PC every time you want to print something. I consider that an unforgivable kludge; at that point, you might as well just sync your iPad.