Is school responsible for a fall over an extension cord?

If you work for the school, file a workers compensation case. If you do not work for the school, contact the school's insurance company and tell them about the incident and the bills. If they do nothing, file a personal injury case.

Slip and fall cases are, by their nature, difficult. First, you must be able to prove negligence on the part of the property owner/occupant. Negligence could be defined as the failure to use REASONABLE care; the owner is not a guarantor. To do this, you must be able to prove that the owner put the slippery substance there, or that they had prior knowledge of the hazard and failed to take care of it promptly. Second, they will claim "comparative fault", meaning that you had a duty to watch where you were walking, and thus are partly at fault. The result is that most lawyers are reluctant to take a slip and fall case unless there are substantial damages, and there are at least some arguments to be made on the question of fault. The above is my generic slip and fall response; trip and fall cases are the same. With a fracture, I don't think you'll have any problem finding a lawyer to represent you.

Yes, it appears that you do have a potential claim against the school, but keep in mind that you have a shortened time within which to protect the statute of limitations if you are making a claim against a public school. If it is a public school, then you need to file a timely claim with the correct governmental entity and school district. This needs to be filed prior to the filing of a lawsuit. Once the government claim gets rejected, then you have a limited time to file the lawsuit. You should consult an attorney regarding the protecting of the statute of limitations as soon as possible.

Possibly. The date of the incident is extremely important for the purpose of a claim against a public entity.