Explain why the mass of a tree cannot be converted directly into energy.
That's a tricky one, because it could turn out that it is possible to turn matter alone into energy. Floris hinted at this with radioactive decay, but there are potentially other methods such as melting hadrons in a quark-gluon plasma (QGP), see for example this report. The interesting thing about that, is that the quark-gluon plasma is something like pea soup. And there aren't any peas in pea soup. See Wikipedia where you can read that the gluons in ordinary hadrons are virtual. There aren't any real gluons in a QGP. It's arguably the same for the quarks. Only then it gets squiffy, because the QGP is allegedly a perfect superfluid akin to a BEC, which features the rather enigmatic Bosenova. Poof! Gone! This might turn out to be a "cheat" which tramples all over the conservation laws. Another possible cheat involves dropping your tree into a black hole, wherein Friedwardt Winterberg's firewall means it turns into a gamma-ray burst. This may involve orthogonal photons and/or neutrinos, but I can't give any references on that. All in all, yes there are laws, but laws do get broken. Where there's a will there's a way, and scientific progress rewrites the law.
Do you always need matter and antimatter to create energy, or can energy be created from matter alone?
Like ACuriousMind said, energy is neither created nor destroyed. That's the law. I know of no way to break this the law of conservation of energy. It's just about the most important law there is. But as to whether the Big Bang was illegal, I just don't know.