I recall when it the single transaction limit was $300 to $400 at some ATMs, this is a safety measure to prevent muggers completely emptying your account in one withdrawal.
There must a more elegant way to transfer funds between accounts, you probably just need the account# and routing# of both accounts to he the bank do the transfer.
Depends what you have set up when you got your debit card .Normally $300-400 ,but you could have asked in your branch for that to be increased . Beside that you can just go in your bank and get as much as you need from teller .
1000$
the daily limit for ATM withdrawals is typically 1k.