Using the bond-fluctuation-algorithm we perform dynamic Monte Carlo simulations on dense symmetric copolymer melts. We cover structures from homogeneous melts to strongly separated regimes. We confirm the scaling laws found in previous simulations for the static properties of the chains and extend these laws into the strong segregation region;The structure factor and various other static properties of the single chain scale with EN. We observe that in the homogeneous phase even for short chains the A- and B-blocks contract due to the prevailing comonomer repulsion. The center-of-mass diffusion of single chains as well as the relaxation of the end-to-end vector exhibit a crossover between two regimes above and below the order-disorder transition. We find that in both regimes the dynamics do not scale with EN. In the strong segregation limit the diffusion coefficient turns out to be lower than the expected value of 2D(0)/3. The end-to-end-vector displays two relaxation processes even well above the order-disorder transition. Besides a fast mode we find a slow mode, more than a decade apart. The simulations show that composition fluctuations above the order-disorder transition have a profound influence on the dynamics.