what do you expect - three questions and three short answers?
What dou you mean by "warping of spacetime in string theory"? The (oversimplified) perturbative treatment of string theory says that gravitons are nothing else but a special (spin-2) oscillation of the fundamental string. In the perturbative picture gravitons do not interact with spacetime (spacetime influences gravitons, but there is no back reaction of gravitons to spacetime, just like weak gravitational waves on flat Minkowski spacetime).
SUSY is an approach to unify spacetime symmetry and "internal" symmetries like isospin or gauge symmetries. This unification is known to be impossible w/o an enlargement of our concept of symmetries. This what SUSY does: it introduces a new symmetry which has conserved charges that behave like fermionic objects and that interchanges bosons with fermions, i.e. acts as a kind of "ladder operator" between particles with different.
(global) SUSY is intertwined nontrivially with Poincare invariance. That means that one can construct spacetime transformations from SUSY. If one tries to construct a local SUSY ("local" in the sense of ordinary gauge theories) than one is forced to introduce a spin-2 degree of freedom, the graviton field; loosly speaking the graviton is the gauge boson of the Poincare symmetry; in addition due to SUSY one must introduce a fermionic partner, the spin 3/2 gravitino field.