Don't use the iPhone, the compass in phones isn't very accurate. They can easily be off by 10 to 20 degrees. As for the level, a bubble level should be more that good enough. As for determining true north, you could use an inexpensive orienteering compass as long as you don't have any ferrous (magnetic) objects near to the compass. However, you'll need to offset the reading using your magnetic declination/variation (varies by you location, you can look up that value on the internet).
Another method is to plot the shadow of the sun during your local (true) noon (i.e. when the sun is due south). I think there are discussions about how to do the latter here on CN.