bought xbox in different region, and now have troubles playing discs

No problem with game discs because the games now are region free, but you will have issue playing DVDs or Blu-ray of different region.

The majority of xbox 360 games are region locked so it sounds like the disc you bought if from a different region than your console.

If it's a region issue as you have stated, then there is nothing that can be done. The disc might be from a different region, and the blu-ray on the Xbox One is not a region free player, so cannot play movie discs from another region.

Xbox 360 Disc games are region locked so it appears the Disc that you bought was for a different region then Saudi Arabia so the best thing to do would be to return the game to where you purchased it and explain it to them.

Also I thought region issue comes only when you put the disc right? Is it the same for game bought via xbox marketplace?

Yes, as the download games are basically "images" of an actual disc, the console is tricked into playing the game from the hard drive, but "thinks" it is an actual disc in the drive (that's why you also get unreadable disc errors, even though it's a download
game that became corrupted).

So if you bought a console from a different region (e.g. USA or Japan), and you have an account from India, and download a game from the marketplace in India, your console will show you the region error.

Also, changing the language region of the console won't change the region the disc checks. The console region (PAL, NTSC US and NTSC Japan) is based on the hardware and can't be changed.