Do you know anything about fire backs in real fireplaces?

[StepAwayFromCake]

We're in a rental cottage, and there's a working fireplace. We've lit a coal fire, but TBH the back of the fireplace looks a bit ropey. There's a hole low down on one side, and the fire is drawn through it. The very top of the fireback is entirely missing.

The first pic shows the fire being lit, and you can see the flame being drawn through the hole at the bottom.

The second pic shows the fire burning, with the gap at the top and back.

Is this safe?

I am not an expert but i think it is cracked and so will not be protecting your bricks. Google fire backs to buy and see how their photos look, I think yours is unsafe, also chimneys need to be swept at least yearly or the crap inside them catches fire so I would not light a fire until you have it swept and a good chimney sweep will tell you if it is safe.