Which graphic file formats are supported by browsers

Every browser that supports XHTML (Firefox, Opera, Safari, IE9) supports self-closing syntax on every element.

<div/>, <script/>, <br></br> all should work just fine. If they don't, then you have HTML with inappropriately added XHTML DOCTYPE.

DOCTYPE does not change how document is interpreted. Only MIME type does.

W3C decision about ignoring DOCTYPE:

The HTML WG has discussed this issue: the intention was to allow old (HTML-only) browsers to accept XHTML 1.0 documents by following the guidelines, and serving them as text/html. Therefore, documents served as text/html should be treated as HTML and not as XHTML.

It's a very common pitfall, because W3C Validator largely ignores that rule, but browsers follow it religiously. Read Understanding HTML, XML and XHTML from WebKit blog:

In fact, the vast majority of supposedly XHTML documents on the internet are served as text/html. Which means they are not XHTML at all, but actually invalid HTML that’s getting by on the error handling of HTML parsers. All those “Valid XHTML 1.0!” links on the web are really saying “Invalid HTML 4.01!”.

To test whether you have real XHTML or invalid HTML with XHTML's DOCTYPE, put this in your document:

<span style="color:green"><span style="color:red"/> 
 If it's red, it's HTML. Green is XHTML.
</span>

It validates, and in real XHTML it works perfectly (see: 1 vs 2). If you can't believe your eyes (or don't know how to set MIME types), open your page via XHTML proxy.

Another way to check is view source in Firefox. It will highlight slashes in red when they're invalid.

In HTML5/XHTML5 this hasn't changed, and the distinction is even clearer, because you don't even have additional DOCTYPE. Content-Type is the king.

For the record, the XHTML spec allows any element to be self-closing by making XHTML an XML application: [emphasis mine]

Empty-element tags may be used for any element which has no content, whether or not it is declared using the keyword EMPTY.

It's also explicitly shown in the XHTML spec:

Empty elements must either have an end tag or the start tag must end with />. For instance, <br/> or <hr></hr>

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).