Is a neighbour responsible for clearing away large parts of their tree that have fallen on our property during a storm
No
All the parties who share the common fencing are equally responsible for it's repair or replacement. The owner of the property on which the tree was located is only responsible for their "fair share" not for the entire amount.
Depends who owns it.
your mother
If it was struck by lightening or blew over in a storm, that's considered an act of God, and the owner of the fence pays. If someone caused the tree to fall over, that person would be responsible. If the tree simply died IDK, still think it's the fence owner though.
I managed to resurrect the fence after it fell over in the storm
the storm cloud
Look really carefully at the wording in your contract. This will help to answer this question. Chances are you are a renter who has purchased the "option" to purchase the property at a set price at a future date. In which case your landlord is responsible for the damages as long as they were in fact caused by God and the shed wasn't something that you put on the property but was there when you started renting it.
During a storm or Thunder Storm or is it the same?
during a lighting storm the weather is normally cold
That is an act of Nature. No one is responsible (liable) for an act of Nature. Your homeowners policy will not cover it. The comprehensive portion of the vehicle owners Auto Insurance policy would have to cover the damage.