how do the large exchanges connect the bitcoin client with their database and process automated transactions (deposit / withdrawal)?
Do they have an own customized clients or is there a feature in the official one?
How? "Very poorly" is the flippant answer.
Mt. Gox ran what was in effect a custom client. The problem with that approach is that you don't get the updates that go into the regular client.
As for the glue between a bitcoin client and the internal systems of an exchange, that's not terribly difficult (security, on the other hand, is). The exact approach differs depending on the way the exchange is set up. For an exchange dealing in fiat, there would similarly need to be some glue between that side and the internal systems.
