Just like there is a download or purchase option for Windows from their publisher (Microsoft), I could not found any download or purchase option from the official website of android (https://www.android.com/) and their owner Google.
Though there are so many third-party websites letting free download android, I don't think they are trustworthy.
I want to just know, is it possible to download or purchase Android software from any official link of their original publishers? Or the software comes only through in-built with the devices?
First, Android is maintained by the Android Open Source Project (AOSP). What you may know as "Google's Android" is Android plus all those Google Apps (including the Google Frameworks).
Second, you can download the Source Code. There is no such thing as an "Installation CD" because, as you correctly assumed, the installation is very much device specific: other than on your PC, it's not done by transferring "selected files", but by flashing an image (think of Partition Cloning), so it must match the hardware 100% – including drivers for specific hardware etc.
As for purchasing: Above link title already says it, Android is "open source" – so nothing to purchase on that end.