Destroy it, then pick it up.
Unfortunately you can't pick up cake when it has been placed.
Use a bucket
Mine it using a pickaxe (wood or better), then pick up the drop.
If you are looking for a way to pick them up, well, you can't pick mob spawners up. You can only destroy them with a pick but it can give you a lot of exp.
Destroy it, then pick it up.
Unfortunately you can't pick up cake when it has been placed.
Use a bucket
Mine it using a pickaxe (wood or better), then pick up the drop.
If you are looking for a way to pick them up, well, you can't pick mob spawners up. You can only destroy them with a pick but it can give you a lot of exp.
Craft a bucket and Right-click on the water with the bucket.
No, they only pick up blocks that are in the world
then your minecraft is bugged...
You will need the 0.3.3 update.
They can pick up endangered animals or plants, and I suppose if a rare jewel was lying around, they could pick it up.
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.
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.