Simulations of coarse-grained models are used to study relationships among chain motion, composition fluctuations, and stress relaxation in unentangled melts of symmetric diblock copolymers. Measurements of the dynamic structure factor S(q,t) are reported as a function of wavenumber q, time t, and chi N, where chi is the Flory-Huggins interaction parameter and N is degree of polymerization. The function S(q,t) is found to be a nearly exponential function of time, S(q,t) proportional to e(-t/tau(q)), for wavenumbers similar to or less than the wavenumber q* at which the static structure factor S(q) S(q,t=0) is maximum. The relationship between the decay time tau(q) and S(q) is used to define an effective wavenumber-dependent diffusivity D(q) for fluctuations of wavenumber q. The function D(q) is shown to change very little with changes in chi N and to be a monotonically decreasing function of the nondimensional wavenumber qR(g), where R-g is polymer radius of gyration. The linear shear stress relaxation modulus G(t) is inferred from measurements of the shear stress autocorrelation function. At low values of chi N, far from the order-disorder transition (ODT), the modulus G(t) agrees with predictions of the Rouse model. Near the ODT, G(t) develops an additional slowly decaying feature arising from slow decay of composition fluctuations with q similar to q*. The behavior of G(t) near the ODT is predicted nearly quantitatively by a modified version of the model of Fredrickson and Larson (FL), in which the prediction of the FL theory for the slowly decaying component is added to the prediction of the Rouse theory for contributions arising from single-chain relaxation, using the independently measured behavior of S(q,t) as an input to the theory.