The Goldfinch is painted on a panel. In the museum Theo indeed puts a panel in his bag. Near the end when the painting is in a suitcase it is quite clearly on canvas nailed on a stretcher.
It is not possible for a dead person to stay in a sitting position on the floor as all muscles lose their tone or power: the back muscles cease to support the spine and chest.
When Theo listens to the sick girl's iPod, he presses the center button to unpause the music. This is the wrong button; the play/pause button below it would unpause the music.
Forcing someone to throw up after the drugs take effect won't change the level of consciousness or help in any way as the drugs or already in the bloodstream. On the contrary, it is a risky manoeuvre as the overdosed person could inhale their vomit and die of suffocation (Boris, who knows about Narcan and first aid regarding drug OD - as stated in the book - should have known this).