Nobody.
I am renting a trailer and a limb falls on my vehicle while parked on the property who is responsible for the damages
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.
No. This is why landlords require tenants to carry renter's insurance. Call your car insurance provider.
You have to make 3006785 large holes ( the size of a potatoe) to remove a limb
When trees are trimmed and you need to control the branch when (as) it falls, you first tie a rope to it called a 'guy' so someone on the ground can pull it in a particular direction, like AWAY from the edge of a roof/fence/doghouse, etc.
Flexor
remove the dead limb all the way to the base
When it falls off the tree and is no longer alive.
Not necessarily. It can be treated. In many cases though, the limb may have to be amputated. Each case is different.
It is called a 'leaf scar'
Amputation.
Mother nature would be responsible for the damage. Unfortunately though, She does not carry Insurance.