I'm creating a map where it's very important for it to be dark outside.
I have an idea, but I'm not sure it would work. If I built a huge box over the playing area with a dark colored block, maybe dotted it a bit with glow stone to give the effect of stars and a moon and give enough light to see, would mobs spawn 27/7? It seems silly to make a map where you can only play 10 minutes at a time.
Yep, would definitely work as long as the light level at the ground/spawning area is below 7 and players are within the distances for hostile mobs to spawn (ideally 24 to 32 blocks away).
Yes, once the cap is reached, no spawning occurs... unless the ones spawned from before despawn or are killed to make room in the cap. Hostile mobs may despawn on their own once the player(s) are farther away than 32 blocks. You may want to read through this page on the Wiki to get a better understanding of how spawning and despawning works:
I have an idea, but I'm not sure it would work. If I built a huge box over the playing area with a dark colored block, maybe dotted it a bit with glow stone to give the effect of stars and a moon and give enough light to see, would mobs spawn 27/7? It seems silly to make a map where you can only play 10 minutes at a time.
http://minecraft.gamepedia.com/Spawn