With regards to AJAX, as long as you grab the concept that the communication between client and server is asynchronous then that should be enough to get creating with GWT.
If you need db access then you place this on the server (using either GWT RPC mechanism or any one of your favourite server side languages).
To answer your second post I'll explain a little on what happens with your application if you are going straight to producing code for your web server.
First, you write the code in Java (or at least those aspects of Java currently supported - 1.4 syntax and most of java.lang and java.util - 1.5 syntax is hopefully coming in the next release).
So no, there is no Java class or servlet to use for pure client side code it is all stand alone.
If you start implementing server side code, then you are free to use whatever language / technology you want and you just deploy as normal. You can also use an approach called GWT RPC which allows you to write more knitted together code and this does require you to deploy a special servlet to your server to handle the commication/serialization etc but that is a trivial deployment.