Just curious: is matrix picture of quantum mechnaics further used in QFT and superstring theories? It seems like not....
Yes, "matrix mechanics" – known as "operator formalism" or "Heisenberg picture of quantum mechanics" – is used in all quantum mechanical theories. QFTs and string theory aren't exceptions. In all these cases, all the matrices are infinitely large, of course, because the Hilbert space is infinite-dimensional. However, that was true already for the quantum mechanics describing one particle on a line – for the simplest quantum mechanical models with at least one continuous degree of freedom. So QFT and string theory change nothing conceptual about these matters.