Marathonman,
You ask two good questions, but they are very distinct.
1) The process of laterally transferring from SWO to another community is very competitive and can therefore be difficult. Since the transfer/redesignation process is governed through a formal administrative board at Navy Personnel Command, it is competitively based and your performance as a SWO matters greatly. So, you must succeed as a SWO. You can read up on the process here:
http://www.npc.navy.mil/Boards/Administrative/ActiveDutyTransferRedesignation/
2) As a SWO, you will change your duties aboard ship. In your first Division Officer tour, you could stay in one billet, but more than likely you do at least two jobs and sometimes even three. A lot of the switching during a tour depends on your personality, skills and the needs of the Command as determined by the XO and CO. In your second Division Officer job, you'll go on to another Command and do something entirely different again. The SWO mantra is "jack of all trades, master of none." However, all the jobs you will have as a SWO rely on foundation skills applicable to all the jobs aboard ship (and ashore). My first job as a SWO-in-training was Damage Control Assistant aboard a destroyer. On my next tour, I served a Strike Officer doing Tomahawk employment. Completely different jobs, but equally dependent upon basic SWO skill sets. This job diversity has been a key aspect in my decision to stay Navy. I've never had the exact same job twice and I've never been bored.
Cheers,
Bubba