2 x Wire Lines in Ceiling Electrical Box - 2 White/2 Black - 3 of them are always hot
Both switches are single pole. The one with the red wire is going to 1 fixture, and the one with the white is going to a second based on the photos with the hot being the common black. A non-contact volt meter may show power on the wires that is not really there with a load. This is called inductive coupling and happens when a hot wire is run in close proximity to a second wire (this is how transformers work).

This won't be too hard to figure out. Notice that one of the cables black white &amp; ground come in together. With the power turned off connect both blacks together and the light fixture to the 2 whites. Turn the breaker on and the light switch on the right hand side will control this light. 

If you would like to figure out the true feeder with the power off connect a light to 1 set of black &amp; white wires of the same cable if the light comes on with the power restored this is the feeder. If the light doesn't come on this is a switch loop and the black is usually tied to the hot or line side of the feeder and the return from the switch is on the white.