Minecraft – find Iron, Gold, and Diamond in survival mode

The only people who can join your world are people on the same network.

In the options, under Multiplayer, uncheck "Server visible by default". This will make any new worlds you make unjoinable.

Then, enter your world. Pause the game, and click the bottom button such that it says "Server is invisible". Ta-da!

All animals do spawn naturally. If you are having trouble getting them to spawn, I suggest trying this:

As the world is not infinite (not unlimited world area) , an interesting new game mechanic called "animal spawn control" can be used. This includes removing or covering all dirt blocks on the surface of the world (and therefore the grass blocks) except in a small area to control where animals spawn. It will also increase their spawn rate.

Credits to the Minecraft Wiki - Pocket Edition: http://www.minecraftwiki.net/wiki/Pocket_Edition