Zaft

I made an account just to answer some of the questions here.
 
First off, the game saves at Chapter 7 if you're playing Xbox. Therefore, Xbox users get 4 saves.
 
Second, DLC packs are usable in Hardcore mode.
 
Third, I just got the Hard to the Core achievement. Gamertag Zaftx91 , so it's definitely not impossible. I used only my plasma cutter, and saved on chapters 10, 13 and 14.
 
If you have more questions, just post here.