The mall security vehicle is driving places it should not be able to go. After you get the quick charger (MacGuffin's) to charge up the scooter, head back and forth until you see the cart again, then climb to the top of the left escalator (near Berry Delicious) and you can chase it when it passes.
You don't see him at night when the painting is stolen, but the next day he is in the Clown Store.
You can find out by looking at the security videos in the museum Security Room. You will need the time card from the night security guard, who is at the Clown Store.
Go to MacGuffin's to get one of the newfangled quick chargers.
You can exit the mall through the security room, and the blimp is to the left of the mall.
Exit the mall through the security room, then go left to find the blimp.
There is security lighting in the gallery itself, notably above the painting "The Scream".
When the painting is stolen, get the timecard from the night security guard (he's in the Clown Store). Then you can see the theft on the videos in the Security Room of the museum.
YES
Just run past the window when the guard's shadow isn't visible on the shades.
Wait until her shadow moves away from the Security Room window, then run across.
You only have the scooter when you are chasing the security cart around the mall. You use the password (frost) to get it from the Manager's Office, and charge it with the charger device from MacGuffin's. After you chase down the cart, Eddie the snake has the scooter (and may still have it when you leave).
You, the security lady, and the Chief Inspector will review the surveillance tapes at the Security Room in the museum. You will eventually have to locate the night guard, who is trying to cheer up at the Clown Store.