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I have a question here. Lets says we have Nick, who has maybe 1 BTC on his account and Bob who has 0 BTC on his account. Can Nick transfer 10 BTC to Bob's account? I assume no. But what if he creates a pool of miners, each one being a computer (or special bitcoin mining chip) with modified software, which says that every transaction of him is valid? Can he then somehow force his transaction to be checked by the specified it thus sending fake bitcoins?

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No matter of hashpower can allow you to create invalid transactions.

Any block which spends outputs which do not actually exist is invalid, and any peer sending an invalid block is dropped from the network for wasting time. All block contents are checked by every node in the network. Miners only order transactions, they don't provide any assurance of validity.

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