Q: Power lines - No, unless you dangled so low that you made contact with the ground. On the other hand, do birds perch on power lines with one or both feet? They perch with both feet but current does not travel through them, same as the human example
Q: Lightning/trees - Assuming something like a Scots pine, rather than a fir tree. Does the pine tree have better conduction properties than the birch tree? Think I'd be flat on my face, on the ground, in any case. I'd go for the pine tree although I don't actually think any studies have been done on this. It's leaves are pine needles so my thinking is that the electricity would choose this path and is most likely to hit them. Lying down on your face would be the correct thing to do though.
Q) Sauna temperature - It only feels hotter because the humidity will have risen. Easy enough to tolerate 80 degrees in dry air, but 80 degrees in water is a pretty hot experience. Yes, always astounds me when people associate adding water with increased temperate when there is a thermostat on a wall reamining constant.
Q) Water/oil - I'll go for water, seeing as oil floats on water. Yes, although the name oil covers a fairly wide range of hydrocarbons and I think heavy oils may not float (bitumen)
Q) Einstein's equation - E=mc2, but don't know why Yes, it proves energy-mass equivalence.
Q) Twice 0 degrees celsius - Err, 0 degrees Celsius? Then again, 0C = 32F, so twice that would be 64F, so about 17.8C. You were correct in trying to convert to other units. If you think of temperature as a measure of kinetic energy of molecules then they cease to move at absolute 0, 0K. at 0 degrees celsius it is quite clear that this in not 0 movement of molecules. So you have to look at it on the absolute temperature scale. 0 degrees C is 273.15kelvins so double 273.15 = 546.3K. To convert back we take away 273.15K leaveing 273.15. So double 0 degrees celsius is in fact 273.15 degrees celsius.
Q) Existing in two places at the same time - Would like to think so, but would make crime-solving a whole lot more difficult! In theory. If I tell you that tomorrow I am either going to be inside asda or morrisons at 10AM and I will decide by flipping a coin. From your perspective at 10AM tomorrow how many places do I exist in?
Q) Upwards lightning - Assume yes, as it manages to strike aircraft (the closest metal object). Yes, although it a rare phenomenon
Q) Alien/human resemblace - If it is humans deciding if aliens resemble us, then yes. The powers of influence. The answer I was going for was yes as all features tend to converge as there is a finite amount of possible ways for a feature to be expressed and these tend to converge into one common feature.
Q) Experience at earth's centre of mass - Dunno. A frigging great headache? Conversely, weightlessness? Yes, weightlessness.
Q) Soldiers crossing a bridge - The marching rhythm interferes with the bridge's own wavelength, causing severe deformation, or at least, a bit of a wobble. I'd thought it was just suspension bridges, but the pedestrian bridge over the Thames at the New Tate had big problems at first, when people started tramping over. Sort of. If the frequency at which the soliders walk (the driving frequency) happens to be the same as the natural frequency of the bridge it will cause resonance which can result in bridge collapse. By walking out of step of each other this is not a risk.
Q) Plants CO2 - Maybe a bit, although it is primarily O2 that is released. Yes plants release CO2 as they are respiring organisims and respiration emits CO2. Thet also fix CO2 as well but they still emit some.
Well, those are my rambling answers to some of the questions.