@Ali289, you posted this in the wrong discussion room - this one here serves for airbnb announcements about their yearly event, the Open. It’s not ment to be a place open for all posts.
If I understand you correctly, there were two things, a damage claim and you left early. I did not understand the part about the damage. It’s settled?
For the refund, as far as I understand, that’s what happened:
you moved out on October 24th for a medical condition.
This was so urgent, that you had to leave on October 24 but not urgent enough to see a doctor before November 6. That’s 13 days. That must seem very strange to any case worker processing your claim.
what happened was, you left and wanted a refund for medical reasons. That may be a reason of extenuating circumstances, “Force Majeure”. To be valid as such, you need to prove, that there was a condition forcing you to act immediately. If you have to be admitted to a hospital, that would qualify. They would give you a letter stating “Ali xy was admitted in our service from October 24 to November...” The letter does not say for which reason you were admitted, that’s private information.
If you need a service provided only in a big city, like urgent examen or a dialyse or whatever, you could get a confirmation from the lab or hospital, “Alu xy presented himself in our facility on the 25, 28 31...” like you would get it to present to an employer for a leave of absence.
If this was the case, your doctor could write, that he ordered examens from the 24 on and saw you with the results on the 6th. You should have a dated invoice for the lab or can print a history of payment via ameli.fr, if you are insured in France.
If you have no proof at all prior to the 6th, you have to understand, that the host will insist, that the normal cancellation conditions apply.