As you get into Greek, you will find that the grammar is not always correct. Sometimes, like in Revelation, the grammar can be explained by the fact that John is in an ecstatic state and the grammar irregularities enhance the message. But even in non-apocalyptic literature, you will find that the grammar rules are not always followed. This should not affect your view of inspiration. All good writers violate grammar, periodically, for effect, or for other reasons.
Since a word in one language does not line up exactly with a word in another language, translation is often a matter of choosing one meaning or the other, which generally means some information is lost. It also means all translations are interpretive. Words have what is called a "semantic range," a breadth of meaning. They don't have one "literal" meaning. In this passage, is Paul saying Timothy is his legitimate child or genuine child? Is Paul talking about Timothy's legal status or character?
When you have one preposition and two objects, the writer is telling you, in a very nuanced way, that you should be viewing the two objects as a single entity. Not identical, but in some way functioning as one. So when a single preposition governs both "God" and "Christ," what is Paul saying?
One of the many functions of the word ὁ is to turn a phrase into a noun, and one of the of the most common phrases is the prepositional phrase. Matt 24:17 show several examples of this, and it also provides an interesting exegetical issue. If this verse is about Jesus' return and the end of time, then why are the people told to not go back into their houses? Time is over; it doesn't matter what's in the house.