1) QFT does not equal special relativity + Quantum mechanics. There are nonrelativistic field theories and they are used in condensed matter physics. And there can be nonlocal field theories, a field theory is just quantum mechanics with infinite degrees of freedom (a field is defined throughout space time and for each point in spacetime there is a degree of freedom)
2) No String theory is not a special kind of field theory, as people currently understand it at least. String perturbation theory is in the first quantized language, the creation and annihilation operators describe the dynamics of a single string, and do not correspond to creation operators for new strings. Thats not to say field theory does not play a role in string theory, 2d superconformal field theories arise which describe the worldsheet of the string. However in typical relativistic quantum field theory you have 1d field theories on the world line because particles are 0-dimensional
A simple way that string theory is not a qft is that the string theory naturally includes the graviton, while the description of a massless, fundamental, spin two boson in QFT leads to a nonrenormalizable field theory (a linearized version of Einstein's gravity).
3) There is a topic called string field theory, which attempts to describe string theory in a second quantized language (so more like field theory and less like relativistic QM). I suppose you can think of string field theory as a field theory with an infinite number of fields (similar to how the transition from QM to QFT is from a finite number of degrees of freedom to an infinite number of degrees of freedom). So string field theory is a generalization of field theory to describe strings.
I can't emphasize this enough, there are nonlocal field theories, just right a term in a lagrangian like σ(x)θ(y)ψ(z) where x,y, and z are all different points. That interaction is nonlocal!
