Will my UK iPhone receive/send calls and texts while in Japan ?
With your UK sim card? If you upgraded to the official 3.1 firmware, all bets are off.
If you're still running 3.0 or earlier, or you jailbroke your phone, then that depends on what your carrier's roaming relationship is with NTT DoCoMo or Softbank, you'd best find out.
If you jailbroke your phone and it is effectively unlocked, you can use this thread:
http://forums.macrumors.com/showthread.php?t=645157 (and this:
http://www.flyertalk.com/forum/trave...el-asia-2.html)
Will it connect to the internet via 3G ? (I'm assuming I'll have no issue connecting to a wifi connection subject to having access to any network).
Yes, but again via Softbank or NTT DoCoMo. The question is how much you want to pay. The going rate with a RENTAL SIM/PHONE is 128 bytes = 1 yen, so 8 yen for every
KB and
$80 for every
MEGABYTE. The Softbank rental service counter will actively refuse anybody who wants to rent a sim card only and present an iPhone.
Will the GPS work ? (I understand that most GPS-based apps use the internet for maps and information)
Yes -- you don't need the Internet for this. I'd strongly advise you to use a fake APN (mobile profile) to prevent you from sending any data, search for FakeAPN. You can still use WiFi using the profile, so get the maps, cache them, then you can walk around town with GPS.