Contrary to what happens in movies, cars that roll down hills do not spontaneously burst into flames when they crash. The car would have been damaged but would have been otherwise intact, and would have contained numerous fingerprints from Alan as would the cell phone he used.
Banks do not give out large sums of money in cash on short notice. The money would be given in the form of a check, such as a certified or teller check. The check would be made out to Laurie, so it would be of no use to Alan.
When performing a well being check on a resident that had threatened suicide- and notably was distressed over his relationship with a female (Laurie), Laurie would not be permitted to enter the residence before police. Police would secure the residence. This is done to minimize liability in the event Alan would have harmed Laurie and then himself.
Repeated blows to the head with a tire iron would not result in the minor incapacitating injury shown. Additionally, Alan was much stronger than Laurie and would have had no trouble wrestling the gun away from her.
The alarm installer punches in the code 2352, then when Laurie tries it she punches in 2368.
When Laurie reads the suicide message, on screen it says June 13, 2015 at 12:47 PM. When the detective asks what time it was sent, Laurie says last night after midnight. After midnight would have been 12:47 AM.
After hearing the suicide note, the detective says maybe it will help her get a search warrant for Mark's home. Laurie offers to let her in via the spare key and the detective says she can't go in without a warrant. Since the subject made a documented threat of suicide, police are legally able to enter his residence to make a well being or welfare (of the resident) check.
Floyd identifies Alan as the driver of the car that hit him. At night in an unlit parking lot, all he would have seen would be headlights, which would reduce his visual acuity, so he would not have been able to see the driver.