Some of the Google examples you cite don't use XML at all. Do I have to use XML and/or XSLT in an Ajax application?

No. XML is the most fully-developed means of getting data in and out of an Ajax client, but there's no reason you couldn't accomplish the same effects using a technology like JavaScript Object Notation or any similar means of structuring data for interchange.

Are Ajax applications easier to develop than traditional web applications?

Not necessarily. Ajax applications inevitably involve running complex JavaScript code on the client. Making that complex code efficient and bug-free is not a task to be taken lightly, and better development tools and frameworks will be needed to help us meet that challenge.

When do I use a synchronous versus a asynchronous request?

Good question. They don't call it AJAX for nothing! A synchronous request would block in page event processing and I don't see many use cases where a synchronous request is preferable.

How do I handle concurrent AJAX requests?

With JavaScript you can have more than one AJAX request processing at a single time. In order to insure the proper post processing of code it is recommended that you use JavaScript Closures. The example below shows an XMLHttpRequest object abstracted by a JavaScript object called AJAXInteraction. As arguments you pass in the URL to call and the function to call when the processing is done.
function AJAXInteraction(url, callback) {

var req = init();
req.onreadystatechange = processRequest;

function init() {
if (window.XMLHttpRequest) {
return new XMLHttpRequest();
} else if (window.ActiveXObject) {
return new ActiveXObject("Microsoft.XMLHTTP");
}
}

function processRequest () {
if (req.readyState == 4) {
if (req.status == 200) {
if (callback) callback(req.responseXML);
}
}
}

this.doGet = function() {
req.open("GET", url, true);
req.send(null);
}

this.doPost = function(body) {
req.open("POST", url, true);
req.setRequestHeader("Content-Type", "
application/x-www-form-urlencoded");
req.send(body);
}
}

function makeRequest() {
var ai = new AJAXInteraction("processme",
function() { alert("Doing Post Process");});
ai.doGet();
}

The function makeRequest() in the example above creates an AJAXInteraction with a URL to of "processme" and an inline function that will show an alert dialog with the message "Doing Post Process". When ai.doGet() is called the AJAX interaction is initiated and when server-side component mapped to the URL "processme" returns a document which is passed to the callback function that was specified when the AJAXInteraction was created.
Using this closures insures that the proper callback function associated with a specific AJAX interaction is called. Caution should still be taken when creating multiple closure objects in that make XmlHttpRequests as to there is a limited number of sockets that are used to make requests at any given time. Because there are limited number of requests that can be made concurrently. Internet Explorer for example only allows for two concurrent AJAX requests at any given time. Other browsers may allow more but it is generally between three and five requests. You may choose to use pool of AJAXInteraction objects.
One thing to note when making multiple AJAX calls from the client is that the calls are not guaranteed to return in any given order. Having closures within the callback of a closure object can be used to ensure dependencies are processed correctly.
There is a discussion titled Ajaxian Fire and Forget Pattern that is helpful.