1) What is supersymmetry (i.e. that which make string theory into superstring theory)?
I'll try to answer this.
Back in the 1970s people were very interested in using symmetries to figure out what theories might describe nature. Symmetries mean that some quantity in the theory is conserved, so I will talk about them that way. Symmetries come in two forms, internal and external.
Internal symmetries mean that things like electric charge, color (American spelling intentional) for quarks are conserved. Internal properties of the particle.
External symmetries mean things like momentum and energy are conserved. They relate to things external to the particle, like space and time.
I should also mention that there are two kinds of particles, bosons which can exist in the same state as each other at the same time (they can pile up in one place) and fermions which will not exist in the same state as each other (they can't pile up in one place).
In the 1970s physicists wondered if you could find an enormous symmetry containing both internal and external symmetries. Two physicists, Coleman and Mandula, showed that this was impossible assuming the algebra in quantum field theory obeyed certain conditions. Later people showed it didn't need to satisfy such conditions and a bigger symmetry was possible, Supersymmetry.
Supersymmetry basically says the theory is exactly the same when you turn fermions into bosons and vice versa. Basically the probability for any collection of particles to turn into any other collection of particles is exactly the same if I switched the type of particle around. Example:
Probability for two bosons and one fermion to turn into three fermions
equals
Probability for two fermions and one boson to turn into three bosons.
Finally the
Haag—Lopuszanski—Sohnius theorem was proved which shows that Supersymmetry is the biggest symmetry you can have if you want the theory to be a quantum field theory. Any bigger and it would have to be something else.