Quote from: ThiagoCMC on July 01, 2011, 09:48:55 PM

Sorry, I'm confusing, because I'm a newbie in Bitcoins world, just two weeks of knowledge about it...

Thiago, I had similar concerns when I was a noobie as well. Most of the answers to your questions are well documented in the bitcoin wiki and faq, or have been answersed extensivly in this forum, which you can easily search the achives for answers. I will give quick incomplete answers below:

Quote from: ThiagoCMC on July 01, 2011, 09:48:55 PM

Until today, I believed that miners only do mining... What they do more? Why miners are so important to keep the safety of the Bitcoins network?

The process of mining is essentially verifying the legitimacy of transactions. The more GPUs mining for bitcoins, then the stronger the legitimate network is, thus making it very difficult for adversaries to overcome the strength of the network by passing off bogus transactions as legitmate.

Quote from: ThiagoCMC on July 01, 2011, 09:48:55 PM

If miners cash-out someday, this will leave the network unprotected.. But why?!?

But when a lot of miners "cashes-out", then the bitcoin client will automatically lower the mining difficultly level based on a hard-coded protocol. Since it will now be easier to mine, then that means that other people, including noobs like yourself, would be incentivized to mine at the easier difficultly level, since the bitcoin payment for solving a block would remain the same (50 BTC/block solved currently).

Quote from: ThiagoCMC on July 01, 2011, 09:48:55 PM

By the way, then it is possible spend the same Bitcoin twice?! Since I have enough computing power for this?

As has been discussed many time, it would be REALLY REALLY difficult and expensive. At this point, only a huge collusion of powerful governments and corporations would be able to do it. Keep in mind, there are tons of teenagers out there with free GPU & electricity from their parents who can hash for basically zero cost (to them, not to the parent

). Plus all the thousands of businesses out there who deal with bitcoin and thus are incentivized to mine and maintain network security.

Quote from: ThiagoCMC on July 01, 2011, 09:48:55 PM

And then it is also possible reverse the payment?!

Yeah, but again...very hard. And you couldn't reverse all payments, just a few recent ones if you are sucessful.

Quote from: ThiagoCMC on July 01, 2011, 09:48:55 PM

All depends on the computational power?!

pretty much. And network bandwidth.

Quote from: ThiagoCMC on July 01, 2011, 09:48:55 PM

If the U.S. government and Fed tries to do these things today?! We are fucked?!

Possibly. They would have to retool all the US government supercomputing research centres in order to mine for bitcoin. But I almost feel at this point, there is are more legitimate ordinary people mining GPUs that the US government would be incentivized to instead join us legitimate miners!

Quote from: ThiagoCMC on July 01, 2011, 09:48:55 PM

I'm very curious and concerned!

Thanks!
Thiago

No problem. Again, I had similar concerns when I was a noob as well. Anyway you get a gold star in my book for using Ubuntu Linux and for asking simple & clear, but non-trolling questions/concerns.