Take it to Performance and have them measure the opening, I'm very surprised they have not done this. (Are you planning on replacing the seatpost, if so, why?)
As for the handlebar swap, in my opinion, I would leave the bull horns, I personally prefer bullhorns (I too, am away in college). Not to mention, if you swap it out, assuming you want your son to run a brake, you will have to buy new road levers, which is simply an extra cost.
But beyond the price, for a college kid, I would imagine that he would find himself on the tops of the bars or on the hoods about 80% of the time. Bullhorns take advantage of these common positions from drops. However, this is my opinion, if anything, I would let your son try it out as is for a week or two, see if he likes the bullhorns or wants to try the Road Drops. No need to replace something if it's not broken (or disliked greatly).