If i create a wallet, get address and then close wallet for a month.
If during this time me and someone will send coins to the address, could i verify its balance via blockchain.info for example?
Does the bitcoin network knows about my address balance, while my wallet is offline ?
To check the balance you can go to
http://blockchain.info/address/BTC_ADDRESS_GOES_HERE and yes even if you wallet is offline, the balance will show since it is still logged on the blockchain.