Yes landlords are supposed to take care of all exterior house maitenence.
Typically, you are not responsible for the maintenance of a rented house. The responsibility for this falls on your landlord. However, read the rental agreement to be sure what you are/are not responsible for.
The livestock owner is.
As I understand it, the landlord is required to maintain it essentially in the condition it was in when you moved in. So if there were working appliances when you rented it, they are responsible for the maintenance. If you are asking is the landlord required to provide new stuff when you move in, no.
Landlord.
Read your governing documents to determine the boundary that defines ownership of the strip in question. If the HOA owns it, the HOA is responsible for its maintenace. If not, then whoever owns it is responsible.
If there was a hazard on the steps because of poor maintenance.
The landlord
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.
The owner of the fence or the owner of the property on which it stands.
Anywhere I've ever heard of the landlord is responsible for this.
Yes, the landlord is responsible. But keep in mind that this is not a landlord/tenant issue: it's a small claims issue. So this is heard in a small claims court inquired, not a landlord/tenant court.
no notice is needed if there is an emergency for maintenance need. THE landlord may enter for any maintenance without tenant's approval after 24 hour notice.