Learn Russian: Здесь нельзя курить, потому что нельзя нарушать закон. - It is forbidden to smoke here because it is forbidden to break the law.

When нельзя is followed by an imperfective verb, it means the action is prohibited or forbidden. Because we are talking about rules here, we need the imperfective to express that you are not allowed to smoke or break the law.

What would it mean if we used the perfective verbs покурить and нарушить?

If you use нельзя with a perfective verb, it changes the meaning from 'forbidden' to 'physically impossible to achieve'. For example, нельзя покурить would mean you literally cannot manage to smoke right now (perhaps you lost your lighter, or the wind is too strong).

Does the negative word нельзя force закон into the genitive case?

No, the 'genitive of negation' is optional and much less common with impersonal words like нельзя. The verb нарушать takes a standard direct object in the accusative case. Since закон is an inanimate masculine noun, its accusative form is identical to its dictionary form.

Can I use нарушать to say I broke my phone or a window?