Dave,
I honestly don't know what requirements you will face during OCS since I didn't go through that training. Though during your swimming at API you will have to jump off a tower into the water, and swim underwater for ~25 feet. Basically simulating escaping from a ship or wreckage, and avoiding any possible oil slicks and flames that would be around the wreckage.
You are primarily concerned with increasing lung capacity. You would surprised how quickly you can improved your ability to hold your breath and swim greater distances under water just by increasing your cardiovascular workout. Either running, or preferably swimming laps at a decent pace over a period of 2 weeks will show a marked improvement in your ability to hold your breath. You are probably already doing this, but I used to always practice swimming under water during my workouts and try and increase my distances.
Is there a good time? No, not really, it is not like you are going to dive school where you will be stuck at the bottom of the pool with your twin 80s and regulator stolen from you by an imposer! Some of the dive school instructors could hold their breath for some serious time, past the 3 minute mark, though fortunately we weren't subjected to that long a period stuck on the bottom without air. But I would say that generally everyone should at least be able to swim underwater without difficulty, the length of a 25 yard pool.
Does exhaling underwater help or hurt you? Well, that is really up to your own technique. I personally exhale along the way in small bursts, but not down to a completely empty lung.
A lot of people before holding their breath or swimming underwater, take many deep breaths, or rapid breaths, basically hyperventilating. (Going back to my dive physics and medical days, so hopefully I am remembering everything correctly!) Basically the person is decreasing their CO2 levels in their body, the craving/desire for air when you are underwater stems from an autonomic response to CO2 levels in the body (higher the CO2 level, the greater the desire to gasp for air).
This technique is ok in the pool, but is VERY dangerous when people do it out snorkling or free diving. The diving community has had its fair share of fatalaties to divers egging each other on to see who could dive the deepest and longest without scuba gear. Sometimes people will come upon a situation called "shallow water blackout", where right as you come back up close to the surface from your breath holding dive, due to pressure changes, the lungs basically suck the O2 right out of your blood supply, causing you to black out at a very shallow depth of 15 feet or so. Very dangerous.
Here is an interesting article about free diving and shallow water blackout, talking about what exactly hyperventilation will do to you (in better terms than what I just described): http://www.gulftel.com/~scubadoc/Freedive.htm
Have a chance to go to dive school? Hmm, I honestly don't see how you could swing it, since you will never be in a job category where you will be required to use that skill. Hey, stranger things have happened, but I kind of doubt it. Basically, all my Navy dive quals lapsed a couple of years ago (my civilian dives don't count unfortunately), and I would either have to get evaluated by a dive locker, or go back through the program if I were ever to be in a position to dive again for the Navy (doubtful!).
But if you ever get the chance, I strongly encourage going through dive school. It is a great community, and a wonderful experience for those of you that are masochists out there! jk Probably the best school in the Navy that I have been through.
Otherwise, sounds like you are doing everything that you need to do to prepare for OCS and API, so basically, don't sweat the small stuff or the fine print so to speak!
As for me, just finished SIM1 yesterday, have two more SIMs to go, and I get to fly the P3, woohoo. Haven't flown since last September, so really looking forward to going out and flying again.
