taking a crack at a few...
Does Mac OS has a concept similiar to Windows Desktop ? Yep. It's called Desktop too, located in your user directory.
Can we put shortcuts, folders and other stuffs on Mac OS desktop (assuming it has a one) ? Yep. You can save stuff to Desktop, or drag a file or folder from a Finder window directly onto the Desktop. Shortcuts are called Aliases. If you right click (control click) any file, one of your options is Make Alias. That will get you a file called "myfilename alias" which you can drag onto the Desktop.
On Windows, we click on My Computer icon to view the contents of the HD, in Mac OS, it called Finder, AFAIK. You can also click on the hard disk icon on the upper right of the screen. That opens a Finder window. (I think of Finder windows as equivalent to Windows Explorer windows, though they don't behave exactly the same.)
But when clicking on Finder, what we see ? partitions labled some thing like : /user /bin ..... (instead of C: D: E: ... on Windows) ? If you open a new Finder window (apple + N) on the left side you get a list of locations, each with an icon. On the right, what you see depends on which of 3 types of view you've chosen.
Any screen shots ? Do you mean how do you make screen shots or do you want someone to post screenshots of a Finder window?
When installing Mac OS, do we need to change the partitions (size for example) ? You don't need to but you can if you want to. It's up to you. (A little known rule of thumb that I learned the hard way:
you should keep 10-15% of your hard disk free to keep the file system happy. I'm not sure if or how that would apply to any individual partition.)
Do you have a Mac already or are you considering moving to it?