Can I ask the school to be responsible for his medical bill if accident happened at the school?

Sure you can ask. The answer will be, no. It is up to you to prove negligence; the failure to use reasonable care. You haven?t told me what the school did that was unreasonable. The school, on the other hand, will say that your child should watch where he walks.

The school likely has no apparent liability in contract or tort but it may have no-fault medical insurance for incidents like this and it might volunteer to pay the bill even if it doesn't have to do so. There may be evidence/facts suggesting liability.

The school only would be liable if they were negligent, which depends upon factors which you do not give us such as was the backpack there for long enough of a time that they should have known about it and moved it, who put it there, could he have seen it if he had looked reasonably around, in what part of the school was it located [a closet where backpacks are placed, in a crowded hallway, etc.].

Yes. The school district is possibly liable for both his medical bills and pain and suffering. However be aware that in California a formal claim needs to be made and filed with the district within 6 months from the date of injury.