Electrical – Is this thestery cable safe

It sounds like they have a floating neutral in the power. If outside at the cable junction box take a look at the connectors. If they are burned or melted then it is a floating neutral and the power in the house looked for a ground which the cable lines are grounded with the house electric. This allowing the cable to get energized which can cause the fire

I agree with @paul: the room should be adequate for protection from a tornado.

However, a bomb shelter was/is designed with different assumptions than what one would design a storm cellar for, primarily that once the bomb shelter is occupied, that there would be no hurry in opening the door for quite awhile. Also that there is little need for outside communication since it is generally assumed that the phone company is gone and probably all radio stations.

A hollow core door is something of a concern due to over-pressurization and under-pressurization between the room and the kitchen during a storm could (and probably will) bust up the door and turn it into nasty projectiles. A nice heavy solid core door is much more likely to perform satisfactorily. It is possibly better to have no door than a hollow core.

Items to consider adding:

• A cell phone repeater located just outside the shelter should easily be able to receive cell phones from inside where the 12–24 inches of concrete might make cell phones otherwise useless.
• A pry bar, handsaw (for cutting lumber), hacksaw (for cutting rebar), and sledgehammer would be good insurance inside to be sure you can get out when it is time.
• Several battery powered lights
• Plenty of water and food
• A porta-toilet
• First aid kit
• You are carrying your cell phone into the shelter with you, right?

In all likelihood, you would be in the shelter for only a few minutes less than once a year. But having the supplies to be comfortable for several days is great insurance even for non-tornado events when you wouldn't even use the shelter.