If i download an xbox 360 game from the disc and after i saved a game i delete it and buy...

Yes. You'll be able to use the same save is if you purchase the game digitally.

I'd already tried downloading the game to the internal disc, but that didn't make any difference. What I have done is delete the saved data from a previous 360 game, which seems to have cleared enough data from the cloud to let me scrap a new save game
file. There's barely any space there though. I've tried putting some old 360 discs in the one, to see if I could access the old saved game data in the cloud so I could delete it and free up some more space, but no saved data was listed. I've already deleted
the local 360 saved games. Can you think of another way of clearing some space in the 360 cloud? I think I still have the 360 in the attic.

Although to play the game that was installed from the disc you have to re insert the game every time you play the game. If you are wondering if you game save will stay with the game you played from the disc when you switch to the downloaded copy, it will.
example, I had FH1 on my Xbox 360 via disc... lost disc... purchased the game when it was free. game save stayed with me and played even when I was on the digital download copy.-- same applies with Xbox one.

So if I were you go to games and apps> go to FH3 box> hit menu on controller> hit manage> Delete the Game but not the game save from the cloud. (do this if you don't care about the internet connection-- if you do care attempt to purchase the game and play
the title as Stuart says)

After you purchase and download the game you will be able to play Forza Horizon 3 with out having the data loss from disc game

Hope that helps

If you delete the game and download it with a different disc I don't think it will save because it is a different data disc, when you buy a used game you start off the game with the beginning of the game because its a new data disc for your Xbox, hope this helped

I'm having the same problem playing off the disc. When I first played the game it started up fine but then unable to read after creating a save. Deleted the game saves from Xbox and bought a new disc and same thing: stopped working after first save.