Is it possible to copy Android OS from my friend's device and install it on my tablet? After encountering a serious problem in my Android tablet, I need to reinstall my android. There is no OS available for my tablet on the the internet. My friend has the same Android tablet. 

So I was thinking if it is possible to 'copy' the Android OS from his device and put it on mine. I have a Porto 9" tablet running android 4.2 and is rooted.
Given that you and your friend both have the same tablet, this should be possible. Your friend will need to be rooted as well. Probably the easiest thing would be for him to perform a Nandroid backup which you then transfer to your tablet and restore.

If this works, your tablet will be in the same state as his at the time he flashed, so you'll need to delete his account, establish yours, etc.

Disclaimer: as with all things flashing, I can't guarantee that this won't make your situation worse. But it sounds like you're already in a bad way.