Wireless networks run on a set of channels (1 to 11 in the US, up to 14 in Japan). If your AirPort Express is set for the same channel as the wireless router you're plugging into, there WILL be interference and neither network will work. Fortunately most devices come set to channel 6 or 7 by default, so if you set your AX to channel 1 or 11 that should make it work just fine. This is done through the AirPort Admin Utility, by the way.
Wireless printing is a bit of an issue, especially with USB printers. However, if your printer has the appropriate drivers (as in drivers that take into account networking the printer), it should work fine.