Although it’s unlikely that the issue might stem from the disk itself, it could be related to the console’s optical drive as it’s failing to read the disk at times, which in return may lead to all sorts of issues similar to the ones you’re experiencing.
As mentioned before, it’s also possible that there’s an issue with the console’s hard drive, would you be able to try and run the game from an external drive just to dismiss this possibility?
Alternatively, could you try to download the game from the store to your console through your friend’s account?