After your last reply it did not look like it had been updated, but maybe it was just cached in my browser. I've hard refreshed the page, and started the game, and it does look like there are changes. I still had a bunch of money from the last play, so I reset and started fresh.
The back button no longer locks up the game, though it does take me to the main menu, rather than back to the pause menu and being able to resume the game. It is just 1 press to continue playing from the main menu, so not a big deal, but generally I would expect a back button to take me back to the screen it came from.
I started playing through the tutorial area. I got to the block you need to switch realities to move, after using a key. I moved it part way and then switch realities and died in the night reality. This brought me back to the start point. The opening text displayed, and then the game froze. I was at 0.85% complete, 91 coins, 1 key, and one of the new gold fragments.
I refreshed the page and pressed play. It loaded me back at the start, with no progress or collected items.
I redid it and died in the day reality this time. This time I was paying attention and it was the blocks that are only safe for a short time that killed me. I think that your decision to have ending a dialog move you is problematic, especially next to these blocks. I'm not a fan of ending the dialog moving you, but if you want to keep it, then you need to design it so that it does not move you onto a danger spot. In this case you can add 1 safe space to the right of the person so ending the dialog moves you there. This will let the player see what happens and then shift to get past. Obviously the game locking after dying here is a bigger issue than the push onto the unsafe tile.
I restarted again, and got to the person who says to get the gold fragment down from them. Closing the dialog by pressing Space moves me to the right 1 tile. Moving back to the tile opens the dialog, repeating the cycle. I cannot go down to get the fragment, nor can I move back to the left to talk with anyone else.
At this point I'm guessing that this forced movement to the right is a bug, as it is interfering with completing the game.
I moved ahead and crossed a checkpoint before intentionally dying, and it did respawn me without locking up, so it may only be an issue with the initial area.
I'm going to stop my replay here, as the movement on closing dialog seems like it is going to be problematic going forward.