Somebody back in the 18th century cobbled together the rule about split infinitives out of whole cloth. There is no good reason in English to avoid splitting the infintive completely and no reason to default to not splitting the infinitive. I would say that if you're going to have a default position make it that of splitting the infinitive, avoiding it only when to split gives an awkward construction.

As for 1) and b) I would say that either is OK but that, to me, b) sounds better.