Ising models, and the physical systems described by them, play a central role

in generating entangled states for use in quantum metrology and quantum

information. In particular, ultracold atomic gases, trapped ion systems, and

Rydberg atoms realize long-ranged Ising models, which even in the absence of a

transverse field can give rise to highly non-classical dynamics and long-range

quantum correlations. In the first part of this paper, we present a detailed

theoretical framework for studying the dynamics of such systems driven (at time

t=0) into arbitrary unentangled non-equilibrium states, thus greatly extending

and unifying the work of Ref. [1]. Specifically, we derive exact expressions

for closed-time-path ordered correlation functions, and use these to study

experimentally relevant observables, e.g. Bloch vector and spin-squeezing

dynamics. In the second part, these correlation functions are then used to

derive closed-form expressions for the dynamics of arbitrary spin-spin

correlation functions in the presence of both T_1 (spontaneous spin

relaxation/excitation) and T_2 (dephasing) type decoherence processes. Even

though the decoherence is local, our solution reveals that the competition

between Ising dynamics and T_1 decoherence gives rise to an emergent non-local

dephasing effect, thereby drastically amplifying the degradation of quantum

correlations. In addition to identifying the mechanism of this deleterious

effect, our solution points toward a scheme to eliminate it via

measurement-based coherent feedback.