Hi Troy - In answer to your questions:
No, it will not sharpen a swivel knife blade. The blade is just too small to work with. The good news is, if you don't drop or otherwise damage your swivel knife blade, all it should need is stropping. If needed, there are special guides made just for swivel knife blades, which can be purchased through a leathercraft supplier.
Sharpening a knife with the blade beveled on just one side is no problem. But since the system is designed to work with knives that have the blade edge running along the long side of the blade, I think you'll have to use a bench stone for a skiver.
I just looked at Lansky's webpage and wow, they have really added to their products. A lot more to pick from now. The Deluxe 5 stone system for $49.99 is the one I have, but it may not be right for you.
If you're going to be using it to maintain blades that you buy new, the 3 stone system is all you need.
If, like me, you buy some used knives, then probably the 5 stone system is the way to go. I bought some great, 100 year old C.S. Osborne head and round knives off of ebay. Great steel, but over the years the blade edges were in terrible shape and it took all five stones to make them right. But brother, do they slice through the leather.
Lastly, if you plan to sharpen knives for others, or your work load is such that you'll be using the system weekly, then you might think about getting one of the higher grade systems.
Let me know if you have any other questions.
Fred