It may vary from person to person, but here's a general answer:
1. You will get a bit of a gap between OCS and reporting to a ship, but I would only plan for a couple of weeks before having to report and then be pleasantly surprised if you get anything more. It will depend on the schedule of the ship you're going to, etc.
2. I was a Submariner and did not go to OCS (USNA instead), but it is my understanding that you get to put in your preferences for which ship type, location, and individual unit you'll go to when you're at OCS. Hopefully someone can confirm that for you, but that would check with how SWON's do ship selection at USNA and I don't know why it would work any differently.