I'll try to answer your questions in the same order:
1) As Jolly roger said, the course you're thinking of is now called NETPO. It's a basic introduction to shipboard life and procedure. It has a strong emphasis on safety. The physical parts are the firefighting and damage control, which we take very seriously. If the ship's on fire or sinking, everybody's having a bad day. There's is also some liferaft training. The mental aspects of all this come into play when you're placed in charge and have to coordinate the fighting of the fire, flood, etc. However, this doesn't stop in NETPO and in fact you will be assessed in this area as long as you continue to go to sea (you also have to do refresher courses every two years).
2) Naval Logistics Officers initially specialize in both finance and supply as those are the two main areas you need to know in order to be a ship's supply officer. Once you are certified "AILK" (this doesn't stand for anything - it's just the code we use meaning that you're qualified to go to sea as the Head of the Logistics Department on board) then you can ask to be posted to finance job if you wish. Having an accounting designation may help the Career Manager make a decision, but in the end, it will be the "exigencies of the service" that will prevail. Note: whenever someone uses the phrase, "exigencies of the service," it usually means you won't like the answer. ;D
3) All Naval Logistics Officers will do at least one tour of approximately one year. This is your "baby" phase where you are the "Baby Supply Officer," more properly known as the Assistant Supply Officer. Even that title is a bit of a misnomer as you are not really an assistant, but a trainee. Your job on board is to learn to be the Supply Officer and in that sense you "assist" the Supply Officer in order to learn his /her job. At the end of that year, you will sit before a board of senior Naval Logistics Officers and try to convince them that you know what you're doing. If they believe you, you get your "AILK" (sometimes also referred to as a "D6," which I'm not going to explain right now). Once you are AILK qualified, and provided you are promoted to Lt(N), you join the queue of your peers and wait for the opportunity to go back to sea as the Head of the Logistics Department in a frigate. This would be at least a two year tour, but not everybody gets to do this. The really lucky ones, may get a third tour as a LCdr in either a destroyer or a supply ship. The Fleet LogO is also a LCdr and he/she goes to sea occasionally.
NOTE: In the Navy, "Supply Officer" and "Logistics Officer" are interchangeable. "Supply Officer" is the older, more traditional term and anybody who actually knows anything about it realizes that they do far more than just Supply. In fact, the Supply Officer is responsible for all logistics on board, including food services. In recent years, people refer to them more and more as the "Logistics Officer." One theory is that the members of the "Supply Department" who were not Supply Techs (ie. the Cooks, Stewards and RMS Clerks) felt slighted...
4) When we refer to the number of years in a tour at sea, it is from the day you report for duty to the day you leave for your next posting. Thus a one year tour on board is one calendar year and does not mean one year of bobbing around the ocean. You will be home for a good part of it and of course there will be port visits! :cheers:
5) Don't confuse obligatory service with your VE. The VE is the amount of time you have to serve before you "complete your engagement" and become entitled to certain benefits (eg. severance pay, move, pension, etc). Your obligatory service is the amount of time you have to serve before they even think of letting you out. It depends on your type of enrollment, but generally is only around three years. However, if you get out before your VE is completed, you give up certain benefits. In short, no, you don't have to stay in nine years, but it may well be worth your while to do so.
6) Don't worry too much about the swimming. You will have to pass the basic swim test on Basic Training (and I saw more than one person dog paddle it), but when life expectancy in the water of the North Atlantic is two minutes in January (and three minutes in July), it really doesn't matter how good your breast stroke is.