Is is necessary to do cross training?
Most of the runners I've worked with did not need to do any cross training. The long runs build endurance, and the short runs between, serve to maintain the adaptations. Cross training will improve overall health and fitness, but this does not have any effect on marathon improvement if my training schedule is used.
Are there any cross training exercises to avoid?
On the non running days, it's best to avoid exercises that use the calf muscles: stair machines, step aerobics, spinning. Maximum recovery of the calf muscle occurs when the muscle is not used in a workout for 48 hours.
Are there any cross training exercises that improve running?
Water running can help you improve your running form. As you move your legs through the running motion, the resistance of the water forces the legs and feet to find a more efficient path. See for more details.