Off-duty LAPD Officer Salvador Sanchez shot and killed Kenneth French and wounded French's parents after an altercation at a Costco in Corona. (Courtesy of NBCLA)

The fatal shooting of Kenneth French, 32, by an off-duty LAPD officer Friday night inside a Costco store in Corona has sparked a lot of questions.

Officer Salvador Sanchez of the Southwest Division also shot French's parents. French's mother Paola French remains in critical condition. Russell French is in the hospital recovering. Sanchez has been placed on home assignment.

HERE'S WHAT WE KNOW

Officer Sanchez was standing in a food sample line holding his 18-month-old son in his arms around 7:45 p.m. when there was some sort of physical interaction with French.

French, who was with his parents, suffers from a mental disability and is non-verbal, according to French family attorney Dale Galipo.

Sanchez was knocked to the ground and moments later opened fire with a 9 mm pistol he was carrying, killing French and critically wounding his parents.

The infant and Sanchez' wife were uninjured.

Sanchez has been taken off street patrol in keeping with LAPD policy after a shooting.

Corona Police Chief Geoge Johnstone is worried about rumors as his detectives conduct their investigation: "There has been a significant amount of speculation on social media regarding this incident," he said in a video statement Tuesday. "Most of this information is erroneous and based on hearsay and speculation. This only serves to stir up the public's emotions."

In addition to the Corona Police, the LAPD is conducting an internal investigation to determine whether Sanchez violated department policy. The Riverside District Attorney will decide whether Sanchez should be prosecuted, based on the Corona Police Department's investigation.

HERE'S WHAT IS DISPUTED

Sanchez' attorney, David Winslow, said the officer was "violently attacked" and that the aggression was unprovoked, leaving Sanchez no other way to defend himself and his son than to open fire.

The family's attorney, Dale Galipo, said the shooting was "completely unjustified." He said Kenneth French "pushed" Sanchez, and that right before Sanchez opened fire Russell French stepped between the two men to try to explain that his son had a mental disability.

Winslow said the officer did not identify himself as being with the LAPD before shooting. Galipo said the officer did identify himself as a police officer. This could be important in determining whether the officer could be seen as acting in his official capacity and whether the LAPD and the city of Los Angeles are liable for his actions.

HERE ARE THE KEY QUESTIONS THAT REMAIN

Where was Sanchez when he opened fire? Galipo said he was still on the ground. That has yet to be confirmed by investigators.

How far away was Sanchez when he opened fire on French and his parents? Galipo said based on his conversation with Russel French, Sanchez was five to seven feet away. That too has yet to be confirmed by investigators.

How many shots did Sanchez fire and where did they hit? Galipo said French's father was hit in the abdomen and chest, and his mother was shot once in the back. LAPD Chief Michel Moore said Kenneth French was shot multiple times.

Did Corona police show deference to a fellow police officer by not arresting Sanchez? Chief Johnstone said they decided not to arrest Sanchez at the time of the shooting for several reasons, "including the need to interview numerous witnesses and review evidence."

How long was Sanchez unconscious? His attorney said it was for "at least three to four seconds" and that he was treated at a hospital for "swelling to the head." That's yet to be confirmed.

What kind of mental disability did French have?

Did French recently change his medications? Galipo told the Los Angeles Times he did but doesn't know if that played a role in the confrontation. When asked by LAist, Galipo said he has yet to confirm whether there was any recent change in French's medications.

The investigation "has been somewhat hindered by not being able to interview all the parties involved," according to Johnstone. Galipo said on Wednesday French's mother remained in a coma and was undergoing surgery. It's unclear if other witnesses are unable or unwilling to speak to police.

WHAT KENNETH FRENCH'S FAMILY IS SAYING

This is a Facebook post from Kenneth French's cousin Rick Shureih.

A CALL FOR WITNESSES

Corona police continue to ask any witnesses to come forward with any information they might have about the shooting. Call Lt. Newman at 951-817-5788.