I'm answering your 2nd question:

It's a really easy proof :

You have $C_m=\frac{m}V$ and $C=\frac{n}V$ where $n=\frac{m}M$, thus $C=\frac{C_m}M$

Therefore : $$\Pi=\frac{C_m R T}{M}$$ For $N$ the ions number it's related to biology, the ions are interacting and they cause this pressure, For example if it's $\mathrm{NaCl}$ the ions are $N=2$

I'm answering your 2nd question:

It's a really easy proof :

You have $C_m=\frac{m}V$ and $C=\frac{n}V$ where $n=\frac{m}M$, thus $C=\frac{C_m}M$

Therefore : $$\Pi=\frac{C_m R T}{M}$$ For $N$ the ions number it's related to biology, the ions are interacting and they cause this pressure, For example if it's $\mathrm{NaCl}$ the ions are $N=2$

Thus Van't hoff law is written in Biology and Biophysics textbooks : $$\Pi =\frac{NC_mRT}M$$