I wish to comment on that too.
And I just made five posts where I tried to contribute something

Exactly. But in more detail: If you generate a wallet you are basically generating a (bunch of) key pair(s): a public one (basically this is the receive address) and a private one (which can send BTC that were received by its corresponding public key earlier). No one notices when you do this on your computer.
So, you can generate lots of addresses, but you can't do anything with them (do transactions that clog the network, so someone does notice): unless you have some huge amount of BTC lying around you can send send them some fractional bitcoin. *
If someone else generates an address that is already generated in your astronomical pool, he can just use it. (And you can drain his funds, but this is astronomically difficult, as some else said before)**

* = spamming attack
** = generating lots of addresses: Collision attack
See https://en.bitcoin.it/wiki/Weaknesses, it has lots of information and of course it explains it more elaborately than I do

Well, for miners with limited mining capacity (most of them, including me) it is very useful to have pools. As designed, the system dispenses around 24 hours times 6 times per hour bitcoins: 144 times a day. Each time it 'gives' 50 BTC (total 7200 BTC/day).

But there are many more miners than 144. So, if everyone were to solo-mine, most would have to wait a long time before some payout occurs, and the variance would be extremely high: Many would never receive anything.

Now I assume that every miner would prefer to have a payout once a day (with a stochastic nature of the amount to be paid), instead of the other way around (where the moment is the unknown and the amount is fixed at 50BTC). This is where pools come in.

I think, currently with all these small-scale miners, and exchange rates wildly fluctuating, a useful distribution would be around ten mining pools of equal size. Then each pool would receive, on average, 14 payouts a day (and so could the miners).

In the long term there could be institutional miners that can live with the stochastic nature of their payouts, and with a stable exchange rate, they can solo-mine.

Lots of useful info here:

https://en.bitcoin.it/wiki/Securing_your_wallet

With this you can only see how many bitcoins went to that particular account. And if they have been spent. But every user has many accounts (addresses), so you don't know how many BTC one particular user has.

Hi guys, I'm new here too
I'm one of those who have an all-inclusive contract for their apartment, ha!