I know that this question was asked a long time ago, but just thought I'd give an update and a correction for future people that read this. (please consider that things may also change in future)
Ok, so first of all, you mentioned that a Chunk is 16x16 block around the player. This is incorrect. A chunk is a section of the terrain and is nothing to do with where the player is. The chunk does not move. A chunk is a 16x16x256 (W,D,H).
So for the mob spawning. The quote you gave is correct, however, does not note that it is centred around the chunk that the player is standing on. So 7 chunks in every direction from the border of the chunk you are standing in.
And now for your question :)
Recently, (not sure when it started) height has become even more important for mob spawning and each chunk is split into segments. This is to reduce the amount the game has to render and does this by going up in 16 block segments starting from 1. So 17, 33, 49, etc. This is called the lc value and can be shown on the debug screen (F3). It is important for mob spawning, why? Because any segments in the chunk above the maximum segment that has anything other than air in do not get checked for spawning conditions. This therefore means that there are many less blocks to check which in theory will make your mob grinder or xp farm more efficient.
There is a fair amount more... however, I think this answers what you wanted. At least I hope it does ;) Best of luck guys.
Update for 1.8 and after
Update 1.8 added a 1/16 meter high hitbox to carpets, which made natural mob spawning on carpets impossible. Carpets are now safe.
Thanks @TomášZato for bringing this up!
(There still are some types of "unnatural" spawning that are able to force mobs into carpets, like Village Sieges.)
Before 1.8
Carpet both does not prevent and does not facilitate mob spawning, but it does help in a way.
Carpet is a non-solid block, so, in terms of algorithm, mobs do not spawn on carpets, but rather in. Basically, you can replace all carpets with signs for the same, but more obvious, situation.
Mob spawning alrotihm, simplified, is the following:
- Pick a totally random place (in 3D, not only on the surface) to spawn a pack. It must be a block of air (not carpet).
- Try to spawn several mobs around the pack on the same height. Block underneath must be solid, and the block mob spawn in may be any non-solid block, like a carpet.
What it means regarding carpets: if you have a level floor in a room, and room is surrounded by solid stone, no mobs will spawn even in the dark, as there are no air blocks on floor level. If you have a building surrounded by air, though, mobs will be able to start spawning outside and "leak" onto your carpet floors.
So, glass floors are as safe as they ever were.
Detailed algorithm is on the wiki.
Best Answer
Yes.
Yes.
No.
This doesn't have relevance, but it's based on a mixture of factors which I don't know. I believe it's being inside the "cave" generation chunks.
It picks a random player to spawn it near.