Learn Russian: Чтобы не нарушать закон, мы решили идти пешком. - In order not to break the law, we decided to go on foot.

In Russian, negative purpose clauses (чтобы не + infinitive) strongly prefer the imperfective aspect. Similar to how нельзя + imperfective means an action shouldn't be done, чтобы не нарушать means 'to actively avoid breaking' the law on purpose. If you used the perfective (чтобы не нарушить), it would change the meaning to 'so as not to accidentally break' it.

We made a specific, one-time decision. Why use the imperfective идти instead of the perfective пойти after решили?

Normally, specific decisions do take the perfective (like решили пойти for 'decided to set off'). However, here the focus is entirely on the mode of transport: walking instead of driving. When you want to emphasize the process or the type of action you chose, rather than just the completion of setting off, you use the imperfective.

Since the verb is negated (не нарушать), shouldn't закон be in the genitive case instead of the accusative?

You are thinking of the 'Genitive of Negation,' which is a great rule to remember! However, in modern Russian, it is optional and mostly used for abstract concepts or to emphasize a total lack of something. For concrete, specific direct objects like закон (the law), the standard accusative case is much more common and natural.

Could we just say мы решили пешком and drop the verb идти?