With data mode deactivated and wifi off, you technically shouldn't be able to access any online stuff, so maybe you're seeing cached resources that were already downloaded... that or your phone is acting odd. All you should be able to do with data turned off is send text messages, make phone calls, and use the GPS, but that's about it. Someone please correct me if I'm wrong.
As for the battery drain problem, mine only drains that fast if I'm in an area with little to no coverage. For example, when at work I get maybe 5% signal at my desk, and my battery will drain very fast if I leave everything enabled. I believe this is due to it constantly searching for a signal and boosting power on the antenna. For that reason I usually put my phone in airplane mode until I step out of the building. Doing this will keep my battery at above 90% almost all day. However, as soon as I enable data again it starts dropping fast with the low signal.