None of the answers above are correct. There are many scenarios where you can be rear ended and still be at fault. The classic insurance scam is where the car in the lane next to you, going much slower than you, suddenly jumps into your lane and is struck by your car. In this scenario you would have no fault at all unless you were considerably above the posted speed limit.
In the first incident you describe, the car making the left turn is at fault. He is crossing your path so he must yield to oncoming traffic. However, if he could not see you coming sooner because you had just crested a hill or rounded a curve then you may have some fault because of your excessive speed. When you say "out of nowhere" it makes it sound like this is what happened.
In the second incident you describe, your cousin is correct. She is stopped in the middle of the road. Lights or no lights, people are expected to not strike objects in the road. It is your responsibility as a driver to look where you are going and to avoid any obstacles in your path. There are no lights on pedestrians, animals, or things that fall off the back of trucks. If you can miss seeing something as large as a car then you aren't qualified to have a driver license. The brake lights will make it easier for others to see her car but the lack of lights does not relieve other drivers of their responsibility to pay attention and look where they are going. You are also correct here because it is stupid to not have the lights on. If you get hit it won't be your fault but you will be hurt as much as the people in the car that hits you so why take the chance?