Can anyone help?
The screen goes black if I die and then I need to start the whole chapter over.

Nevermind, turns out you can copy and paste the save files in the folder if they corrupt.

I am getting really bad crashes, corruption and weirdness in Chapter 7. Seems like they didn't do such a good job here.

Firstly, sometimes the game says "Do you want to retry?" and I click Yes and it takes me back, only some inventory items I had before are missing. I did this a few times and lost so many items I had to start over. It also saved my game without me asking so I couldn't go back.

Secondly, one time at least I clicked forward and it jumped backwards in time to a previous scene.

Thirdly, I found that if I click "quit" during Chapter 7 it says "if you quit now you will have to start the chapter again," and I click Yes, and then it promptly deletes my saved games.

I'm pretty glad I made a backup before I started this chapter, and I recommend anybody else does too!
Oh wow, apparently the deleting-your-saved-game is a feature, not a bug. From PDOCO.TXT: "From this point on, your "old" saved game will not exist in the same form anymore. Instead, it will resemble a "saved" movie sequence instead."

So it intentionally deletes your saved game, and replaces it with the "chase" movie. Too bad (at least for me) it was so buggy it got my game into an unwinnable state and saved over everything.
(Weird: I replied to myself and instead of creating a new post, it edited my previous post and added the text to the end. Is this a GOG bug?)