(1) She was pretty good at oral skills, compared to her classmates.
(2) Congratulations, you've asked the 64 billion dollar question!
The "rule" is NOT to split the infinitive.
Properly to prepare my homework...
To prepare my homework properly...
The second version seems better to me.
Purists insist on this rule. In fact, I have heard that when the British and the Americans were negotiating a fishing treaty in the late 1800's, the British diplomats were issued specific instructions not to allow a split infinitive in the final text. I don't know whether this is a myth or not.
As I recall reading, examples of split infinitives occur regularly up to the time of Shakespeare, but rarely after that, until the nineteenth century, when they reappear with a vengeance.
Today they're used all the time.
My opinion, for what it's worth, is as follows. If you find yourself splitting an infinitive, see if the adverb looks better in front of it, or behind it. Say each phrase out loud and see what sounds more natural. If neither sounds good, try to rewrite the sentence in some way to avoid the "To/properly/do" construction. If that doesn't work, go ahead and split.