For future reference, here's my public key. It's the same one that's been there since the bitcoin.org site first went up in 2008. Grab it now in case you need it later.

Bitcoin - Open source P2P money
Bitcoin is an innovative payment network and a new kind of money. Find all you need to know and get started with Bitcoin on bitcoin.org.
The heat from your computer is not wasted if you need to heat your home. If you're using electric heat where you live, then your computer's heat isn't a waste. It's equal cost if you generate the heat with your computer.
If you have other cheaper heating than electric, then the waste is only the difference in cost.
If it's summer and you're using A/C, then it's twice.
Bitcoin generation should end up where it's cheapest. Maybe that will be in cold climates where there's electric heat, where it would be essentially free.
It is possible to verify payments without running a full network node. A user only needs to keep a copy of the block headers of the longest proof-of-work chain, which he can get by querying network nodes until he's convinced he has the longest chain, and obtain the Merkle branch linking the transaction to the block it's timestamped in. He can't check the transaction for himself, but by linking it to a place in the chain, he can see that a network node has accepted it, and blocks added after it further confirm the network has accepted it.
As such, the verification is reliable as long as honest nodes control the network, but is more vulnerable if the network is overpowered by an attacker. While network nodes can verify transactions for themselves, the simplified method can be fooled by an attacker's fabricated transactions for as long as the attacker can continue to overpower the network. One strategy to protect against this would be to accept alerts from network nodes when they detect an invalid block, prompting the user's software to download the full block and alerted transactions to confirm the inconsistency. Businesses that receive frequent payments will probably still want to run their own nodes for more independent security and quicker verification.
It might make sense just to get some in case it catches on. If enough people think the same way, that becomes a self fulfilling prophecy. Once it gets bootstrapped, there are so many applications if you could effortlessly pay a few cents to a website as easily as dropping coins in a vending machine.
If you can keep a node running that accepts incoming connections, you'll really be helping the network a lot. Port 8333 on your firewall needs to be open to receive incoming connections.
Any owner could try to re-spend an already spent coin by signing it again to another owner. The usual solution is for a trusted company with a central database to check for double-spending, but that just gets back to the trust model. In its central position, the company can override the users, and the fees needed to support the company make micropayments impractical.
Bitcoin's solution is to use a peer-to-peer network to check for double-spending. In a nutshell, the network works like a distributed timestamp server, stamping the first transaction to spend a coin. It takes advantage of the nature of information being easy to spread but hard to stifle.
Bitcoin addresses you generate are kept forever. A bitcoin address must be kept to show ownership of anything sent to it. If you were able to delete a bitcoin address and someone sent to it, the money would be lost. They're only about 500 bytes.
At first, most users would run network nodes, but as the network grows beyond a certain point, it would be left more and more to specialists with server farms of specialized hardware. A server farm would only need to have one node on the network and the rest of the LAN connects with that one node.
The incentive can also be funded with transaction fees. If the output value of a transaction is less than its input value, the difference is a transaction fee that is added to the incentive value of the block containing the transaction. Once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees and be completely inflation free.
At first, most users would run network nodes, but as the network grows beyond a certain point, it would be left more and more to specialists with server farms of specialized hardware. A server farm would only need to have one node on the network and the rest of the LAN connects with that one node.
The traditional banking model achieves a level of privacy by limiting access to information to the parties involved and the trusted third party. The necessity to announce all transactions publicly precludes this method, but privacy can still be maintained by breaking the flow of information in another place: by keeping public keys anonymous. The public can see that someone is sending an amount to someone else, but without information linking the transaction to anyone. This is similar to the level of information released by stock exchanges, where the time and size of individual trades, the "tape", is made public, but without telling who the parties were.
The receiver of a payment must wait an hour or so before believing that it's valid. The network will resolve any possible double-spend races by then.
You could say coins are issued by the majority. They are issued in a limited, predetermined amount.
We consider the scenario of an attacker trying to generate an alternate chain faster than the honest chain. Even if this is accomplished, it does not throw the system open to arbitrary changes, such as creating value out of thin air or taking money that never belonged to the attacker. Nodes are not going to accept an invalid transaction as payment, and honest nodes will never accept a block containing them. An attacker can only try to change one of his own transactions to take back money he recently spent.
A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution.
The price of any commodity tends to gravitate toward the production cost. If the price is below cost, then production slows down. If the price is above cost, profit can be made by generating and selling more. At the same time, the increased production would increase the difficulty, pushing the cost of generating towards the price.
The design supports a tremendous variety of possible transaction types that I designed years ago. Escrow transactions, bonded contracts, third party arbitration, multi-party signature, etc. If Bitcoin catches on in a big way, these are things we'll want to explore in the future, but they all had to be designed at the beginning to make sure they would be possible later.
As you figured out, the root problem is we shouldn't be counting or spending transactions until they have at least 1 confirmation. 0/unconfirmed transactions are very much second class citizens. At most, they are advice that something has been received, but counting them as balance or spending them is premature.
Think of it as a cooperative effort to make a chain. When you add a link, you must first find the current end of the chain. If you were to locate the last link, then go off for an hour and forge your link, come back and link it to the link that was the end an hour ago, others may have added several links since then and they're not going to want to use your link that now branches off the middle.
Even if a bad guy does overpower the network, it's not like he's instantly rich. All he can accomplish is to take back money he himself spent, like bouncing a check. To exploit it, he would have to buy something from a merchant, wait till it ships, then overpower the network and try to take his money back. I don't think he could make as much money trying to pull a carding scheme like that as he could by generating bitcoins. With a zombie farm that big, he could generate more bitcoins than everyone else combined.