In Hive, hits are considered global. Every non-special attack is considered to deal one point of damage. If you lose all hit points, you go down.
A territory mission is any attack/defend style mission set in one of the territories on the campaign map. This can be either pve (player versus environment) against NPC renegades or other monsters, or pvp (player versus player) against another faction or warband fighting for the same territory.
Any mission that takes a warband or player to an area of the Hive that isn't one of the established territories available for capturing/defending is considered non-territory. Certain abilities (warleader calls for example) may not work in this zone. Check with the refs if unsure.