I left some stuff on top of the stove and turn on the oven but the top of stove came on and burned the kitchen up. . The smoke alarm never went off to alarm me .Am I fully responsible for paying all the cost, Is the landlord responsible for the smoke alarm working,

You were clearly negligent, the cause of the fire, and nothing about the structure contributed.
It may depend partly on the kind of smoke alarm. A building with all-electric alarms is one thing, individual alarms with a battery, or wired alarms with batteries, are another. You are responsible for the batteries.
His insurance company will probably deny his claim for the structure, if the fire marshall's report says that he didn't have working alarms. Tenants need their own renter's insurance for contents that belong to them, unless the fire was clearly the fault of the landlord. You have no basis for a suit against him for your possessions, but he may have one against you, and the burden will be on you to defend yourself, based on what the fire report says about the alarms.

Did you know the alarm was not working before the fire?
Was there a annual test of the alarm?
If you knew it was not working, did you notify anyone.

There is no clear cut answer.

I would say expect to be liable for all for the damages since the alarm not working did not cause the fire.

Be sure to notify your insurance company. They might be required to pay the damages.