The Enderman can pick up certain blocks and move them around. Creepers can blow holes in the ground. But apart from these, mobs generally cannot affect the terrain.
So far there is no trading system in Minecraft so all you do is just throw the items on the ground and they can them pick them up.
You can't pick up monster spawners in Minecraft. You can use a mod like too many items to give yourself monster spawners. To break them, the quickest way is a pickaxe
then your minecraft is bugged...
Destroy it, then pick it up.
The item ID for a diamond pick in Minecraft is 278. I have linked you below in the related links of a full list of all the ID's in Minecraft.
Walk close to the object and it will automatically be added to your inventory
You will need a iron pick.
There is no such thing as an emerald pickaxe in Minecraft.
With the original "vanilla" game you can only turn them on or off in multiplayer. There are quite a few Mods that you can pick and chose which ones you want. In single player and multiplayer. They also can make all kinds of different animals too, good and monster.
An Iron Pick :)
go to single play in the main menu, then pick galaxy mode, and pick a character, when you get to the boss with the circle looking slighty different you'll get a new character and a dragon ball, plus every third time you summon shenron, you summon porunga and get 3 wishes.