Also, the computing power is computed from the percentage of successful transaction blocks. Noone knows how much computers you had or anything, they just saw that 15% of the blocks were confirmed by the same PC.

The confirmation task can be easily paralelised - therefore, what is usually done is creating a whole pool of computers that together work on the transaction confirmation task, then the main computer announces the confirmation and is remembered in the blockchain. That's what these so-called mining pools do.

You can browse the blockchain by yourself here http://blockexplorer.com/

There is always at least 1 transaction in the block with the amount 50 - that's the "new" bitcoins that the person "mined" - those weren't previously in the system, you got them for the confirmation. Someone is cheating the system by creating empty blocks with only this transaction.