Zoysia will go dormant at the first frost. If you apply a pre-emergent such dithiopyr to a newly seeded area, it could inhibit the grass seed growth. The best way to determine what grass seed would grow and establish well in your area would be to speak to someone at your Local Cooperative Extentions Office for what will thrive in your weather and environments conditions.
Yes, you can hydroseed using Zenith Zoysia Grass Seed.
Whatever fertilizer you choose for your Zenith Zoysia lawn would be determined by its needs/health and what level of nutrients are present in the soil, as well as the pH of the soil. If the lawn is not majorly lacking in any particular nutrients, a general 10-10-10 fertilizer would be fine to apply as a general feed.