In the toolset under Edit|Module Properties|Events tab|OnPlayerDeath it shows the script that runs when a player dies. It should have something like this to make the respawn screen appear:
DelayCommand(2.5, PopUpGUIPanel(oPlayer,GUI_PANEL_PLAYER_DEATH));
If it is popping up but without the respawn option, then the code probably says this:
DelayCommand(2.5, PopUpGUIPanel(oPlayer,GUI_PANEL_PLAYER_DEATH, FALSE));
The FALSE is telling it to not have the respawn option available.
If the quest updates the faction rep before you want it to then something is causing that. It might be a script attached to a conversation node that you think is gone but isn't. Beyond that, I can only guess. I have quests that update from triggers, when you acquire something, when you disturb something, when you defeat something, when you choose a conversation option, when you destroy something, etc.