Q: What is military?
A: Military is used for planetary defenses building. They are also used for Hyperion Shrinker, Hyperion Logistics etc.
Q: Do research, manufacturing and military production carry over?
A: Yes, they carry over. For example with a shipyard with 1000 military manufacturing points and a ship costing 100 manufacturing points. The shipyard can continue to build 9 additional ships even if you direct manufacturing points away from the ship yard.
Q: On the planet window, what are the number and adjancy bonus?
A: Each tile on a planet may have a bonus to a specific type of resource (wealth, tourism, manufacturing, research, military). A +1 provides a +1 level to the building on the tile. I believe (without actually having tested it) that a basic factory with 25% and a +1 provides another +5% totalling 30%.