Is it obligatory to create a new empty account and send coins to if from the account created online according to previous instructions?
Or can I still use the same, my "first" account to which I've claimed my coins?
Is there any difference?
Yes and no....You can use the same acount but its safer to make a new one on your local client becaus your password could have been recorded/safed/hacked when entering it on the online client.
Its unlikly I would guess, but better be on the safe side