Is it possible to connect to multiple databases simultaneously? Can one extract/update data from multiple databases with a single statement?
As to the second part of the question, one needs special middleware to deal with multiple databases in a single statement or to effectively treat them as one database. DRDA ( Distributed Relational Database Architecture -- I, at least, make it rhyme with "Gerta" ) is probably most commonly used to accomplish this.
Oracle has a product called Oracle Transparent Gateway for IBM DRDA and IBM has a product called DataJoiner that make multiple databases appear as one to your application. No doubt there are other products available. XOpen also has papers available regarding DRDA.