Active Desktop for Windows 7 (Vista)?

Active Desktop for Windows 7 (Vista) - how do I install it on Windows 7/Vista?

Where is analogs? Is there such thing for Mac and Linux?

Is there a browser which can work under icons of desktop?

Windows Vista and 7 do not include Active Desktop I believe. The closest thing to it is probably Ave's DesktopSites:

I'm using Snippage to add live web pages to my desktop via Adobe AIR. It works great.

You can create your own Windows gadget to show a web page on the desktop in Windows 7. It's not much more complicated than creating a simple web page using Active Desktop. You create your web page and an XML document to go with it.

The only caveat I found is that you need to define the width and height of the body tag in your HTML so that Windows displays the gadget using the correct pixel dimensions.

There's certainly no need for 3rd party applications! Here's Microsoft's explanation of the XML file that needs to accompany your HTML. http://msdn.microsoft.com/en-us/library/bb508509(VS.85).aspx