Question: I didn't see any license information on top of a web page's source code. Now I'd like to copy/paste a javascript code to emulate the behaviour of AJAX into my software. 

But can I do this?

Answer: 
At least in the United States, every work is automatically granted copyright protection of its owner, regardless of any copyright declaration or licensing information. You can only be granted rights to use or re-use works under the explicit grant of permissions by copyright owners.

If there's no license on the files, then you have no right to re-use them in your own projects. You're free to *email* them and ask politely, or search around and see if those tools are freely available elsewhere (and the site where you found them stripped off the documenting headers), or to take *inspiration* from their site and try to replicate it yourself.

There's enough excellent libraries out there ([jQuery](http://jquery.com/) and [prototype.js](http://www.prototypejs.org/) come to mind immediately) with enough amazing functionality that you ought to be able to build something cool on your own, in case the owners of the site you found don't want to share their code.
No. Unless you have a license, you don't have a license.

Take a book, it might not be written "You allowed to read it and make a short citation. You should not print copies of it and give it away to people. Neither are you allowed to upload it on piratebay". However, usually you are not allowed to do it.

In most countries, software is covered by copyright as books and other things.