It doesn't really matter whether we call it an adjective or not. The point is that brick and wall co-occur so much, that we register it as a single entry in our mental dictionary. We wouldn't typically call a wall made of concrete bricks or Lego bricks a "brick wall", meaning that the term refers to something distinct from "a wall that's made of bricks". The intonation of "brick wall" is also distinct from "tomato wall", since the latter is pronounced with a rise on tomato. That's pretty good evidence of whether or not something has essentially become a fused expression. Compare how you'd pronounce "cheese dip" and "cheese shoes".

This is a bad example, yes. Brick wall is essentially lexicalized at this point. It's stored in the brain as a single entity denoting a specific thing. This is like asking why you can say a big bluebird, and not a blue big bird.