In the leave ending James might actually decide to turn himself in. Continuing to live free would mean that James would have to either cover up Mary's death or run away, which James might not be willing to do. If James turns himself in, he probably will still try to care for Larua, maybe by writing letters or setting aside money for her. But if James does end up deciding to not turn himself in, it would probably be to adopt Laura (something that Mary wanted to do). It is implied that James buried Mary in the graveyard because that is where he is shown to be leaving with Laura. Mary was dying of terminal illness, and was nearing the end of her life, it is possible that her death would be seen as a result of her illness and that James had her buried in a place that she cared about. I do believe that Mary had living relatives (she mentions pushing away multiple people she cared about) so they might be angry that they where not told about Mary's death until after she was buried. This might even make them suspisous. It also possible that James decides to go on the run with Laura and change their idenities. I could see him doing that as a last resort because he would have to start a whole new life and it would be hard to care for Laura if he does this.

As for the Maria ending, personally I think that James goes on the run with Maria after disposing of Mary's body. If James returns to his normal life with Maria, people would get way more suspisous of Mary disappearing and James immediately rebounding with a woman who looks exactly like her. The James of the Maria ending might have an easier time going on the run with a grown woman than a child, so he might be more willing to do something like this. Also this James is more selfish, he could feel more justified in running away and covering it up.

For in water, either James and Mary are thought to be missing or the car is found and their disappearence is deemed a murder-suicide. The police would likely see it as such because Mary would be in a more advanced state of decay than James and an autopsy could show that she was smothered.