We report on both analytical and numerical results concerning stochastic Hopfield-like neural automata exhibiting the following (biologically inspired) features: (1) Neurons and synapses evolve in time as in contact with respective baths at different temperatures; (2) the connectivity between neurons may be tuned from full connection to high random dilution, or to the case of networks with the small-world property and/or scale-free architecture; and (3) there is synaptic kinetics simulating repeated scanning of the stored patterns. Although these features may apparently result in additional disorder, the model exhibits, for a wide range of parameter values, an extraordinary computational performance, and some of the qualitative behaviors observed in natural systems. In particular, we illustrate here very efficient and robust associative memory, and jumping between pattern attractors.