1. The word "fractal" has no established commonly accepted definition. (Some definitions involve self-similarity, others only Hausdorff dimension).

2. You should specify what exactly you mean by Weierstrass-Mandelbrot. There are several of constructions of continuous nowhere differentiable functions. Probably the simplest one is due to van der Waerden

3. The exact value of Hausdorff dimension of the original Weierstrass graph is not known (at least to me). Some partial results can be found in

MR1002918 Przytycki, F.; Urbański, M. On the Hausdorff dimension of some fractal sets. Studia Math. 93 (1989), no. 2, 155–186.

4. Certainly, there are many nowhere differentiable functions whose graph is not a fractal in any accepted sense.

1. The word "fractal" has no established commonly accepted definition. (Some definitions involve self-similarity, others only Hausdorff dimension).

2. You should specify what exactly you mean by Weierstrass-Mandelbrot. There are several of constructions of continuous nowhere differentiable functions. Probably the simplest one is due to van der Waerden. It is given in Landau's famous Calculus textbook immediately after the definition of the derivative.

3. The exact value of Hausdorff dimension of the original Weierstrass graph is not known (at least to me). Some partial results can be found in

MR1002918 Przytycki, F.; Urbański, M. On the Hausdorff dimension of some fractal sets. Studia Math. 93 (1989), no. 2, 155–186.

4. Certainly, there are many nowhere differentiable functions whose graph is not a fractal in any accepted sense.