None, Trees fall all the time, It's a natural occurrence. Nobody is liable for an act of nature.
Which government is responsible if a tree falls?
Nobody.
NO. A property owner is not responsible for acts of nature.
your auto insurance
If the tree was not dead already and clearly so then your insurance would pay for the damage to your house. A storm that causes the tree to fall is considered an "act of God" and the neighbor is therefore not responsible for the incident.
Depends who owns it.
your mother
When Big Tree Falls was created in 1984.
More than likely God is responsible for the storm that caused the tree limb to fall and damage the shed. Doesn't the landlord own the shed? If the shed belongs to you then you are responsible for repairing the shed. If it belongs to the landlord then he can decide whether or not he wants to repair it.
Weather doesn't matter. Your HomeOwners Insurance would be responsible for those damages.
Hopefully you have full coverage auto insurance with comprehensive. The tree owner is not liable for damage to cars from falling trees unless you could somehow prove that he was knowingly or negligently responsible for the tree falling on your car.
No. This is why landlords require tenants to carry renter's insurance. Call your car insurance provider.