thanks so much! so I need to write down an address from one computer , then go the other computer and type this address in, right? because otherwise there is no other identification?

Hi,
i am new to BTC and still did not generate coins. I have 2 questions and it would be fantastic if you could help me:

1) If I would have Bit coins, how could I transfer or use them on a different computer?
2) What if I shut down or hibernate my computer during the BTB generating. Will all be lost or does the system restart where I stopped ?

thanks!