I don't believe there is an official ledger system. AFAIK the amount owed by/to each bank is reconciled every day and each bank's account will be credited/debited accordingly. I believe it is up to each bank where the money fom each transaction came from/went to
Depends on country.
its not a ledger system in the manner that bitcoin is done. but the banking systems ledger is more like 'bank statements' not used to calculaate totals, but more so to sit beside the balance and be used to question the balance later if any problems occured