How to intercept HTTP requests and responses of a client machine (like fiddler does)

No. The HTML 5 spec mentions:

The method and formmethod content attributes are enumerated attributes with the following keywords and states:

The keyword get, mapping to the state GET, indicating the HTTP GET method. The GET method should only request and retrieve data and should have no other effect.

The keyword post, mapping to the state POST, indicating the HTTP POST method. The POST method requests that the server accept the submitted form's data to be processed, which may result in an item being added to a database, the creation of a new web page resource, the updating of the existing page, or all of the mentioned outcomes.

The keyword dialog, mapping to the state dialog, indicating that submitting the form is intended to close the dialog box in which the form finds itself, if any, and otherwise not submit.

The invalid value default for these attributes is the GET state

I.e. HTML forms only support GET and POST as HTTP request methods. A workaround for this is to tunnel other methods through POST by using a hidden form field which is read by the server and the request dispatched accordingly.

However, GET, POST, PUT and DELETE are supported by the implementations of XMLHttpRequest (i.e. AJAX calls) in all the major web browsers (IE, Firefox, Safari, Chrome, Opera).

If your action is not idempotent, then you MUST use POST. If you don't, you're just asking for trouble down the line. GET, PUT and DELETE methods are required to be idempotent. Imagine what would happen in your application if the client was pre-fetching every possible GET request for your service – if this would cause side effects visible to the client, then something's wrong.

I agree that sending a POST with a query string but without a body seems odd, but I think it can be appropriate in some situations.

Think of the query part of a URL as a command to the resource to limit the scope of the current request. Typically, query strings are used to sort or filter a GET request (like ?page=1&sort=title) but I suppose it makes sense on a POST to also limit the scope (perhaps like ?action=delete&id=5).