> 1. If an electron neutrino can spontaneously transform to a tau neutrino with higher mass, where exactly does the required energy come from? Alternatively, when a tau neutrino transforms to an electron neutrino, where does the extra energy disappear?
It is not yet known which neutrino has the higher mass. Also, when we say electron-, muon- or tau-neutrino we are speaking of weak-eigenstates, something that is well defined at the point of interaction (only). These do not even have a definite mass (they are not mass eigenstates) although they do have a mass expectation value (average, expected mass). Instead they are a super-position of the 3 mass eigenstates. This superposition changes as the neutrino wave packet propagates. This is because each mass eigenstate propagates independently and since energy must must be conserved, each mass eigenstate will travel at different speeds. This propagation then leads to oscillations, or the mixing of weak eigenstates. If the neutrino wave package is detected later, one may see an outgoing electron, muon or tau even if one starts, in the case of OPERA, with a muon-neutrino (and the neutrino energy is at least high enough to produce the outgoing lepton mass).
> 2. If neutrinos have mass, then they are restricted to speeds below c. If they are accelerated to near c, then according to the relativistic energy-momentum equations they should have colossal mass, not miniscule (just like electrons, for example). Is there any evidence of observing neutrinos with huge energies?
Well, particle masses do not change with speed. One can couch relativistic equations into an effective mass, which does increase with speed. But, in any case, only (rest) mass differences matter in neutrino oscillations (differences of squares of masses, actually).
Experiments like IceCube look for and see incredibly and not fully explainable high energy neutrino interactions.