If I deposit funds into IB from my bank account in Bank A in Country A, can I withdraw the funds and request it to be credited into my bank account in Bank B in Country B? Both bank accounts are under my name.
You can but I think if you going to transfer out to another bank, even if its your name, the money must have been in IB for at least 60 days, unsure of the number, but definitely do your homework because what you wish to do won't be allowed right away.
Yes you can,I'm not sure about the minimum holding time Autodidact mention, but a look on their website should give you the answer
If bank B is in another country and currency then you would have a margin loan in currency B if you don't do the currency exchange.