I have a theory about the time loops! Knowing that some thoughts can persist for a short time through a time loop, if you can focus on your dying shortly before the time loop, you could remember that you had died before. Doing this would give you the ability to start finding out who killed you and how to avoid it. Doing this enough times while burning in previous memories from past loops into your mind could eventually give you enough information to either completely dodge the death or kill your killer.
Most of this is probably inaccurate, but this is more of a far-out theory than anything serious.