Maybe i did not catch the idea of Trezor, but lets imagine that I will have one standalone computer with wallet. I need to connect to internet to get incoming tansactions. Or not? Than what exactly tresor do? I thought that Tresor only sign the transaction. Because where is the 20 GB blockchain info?
You will do most of your account management and processing on the computer that is connected to the internet. Only when it is time to sign a transaction, you will transfer the transaction data to the other computer that has your wallet, sign the transaction there, transfer the signed transaction back to the first computer, and broadcast it from there.
The Trezor basically replaces that second computer. It keeps your private keys, signs transaction that are passed to it by your primary computer through the USB port, and returns the signed transactions to the primary computer.
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Is there any chance to find out that someone use copy od my wallet? What will you do as the best secure solution?
I cannot help you there. As it says in my signature, I do not own bitcoins -- mainly for other reasons, but for this reason too: bitcoins are easy to steal, and once stolen there is nothing one can do, no none to help, and no hope of ever getting them back.
There is no way of knowing whether someone has a copy of your wallet, but that is very likely. (The alternative is that a malicious software in your computer sent out the transaction on its own, without sending your wallet to the thief.) Definitely, you should never use those addresses and private keys again.