So the personas inherit powers from the personas that are fused in to them? I almost want to buy a Vita just to play with the delicious systems.
Basically, but it won't inherit things that go against its nature in a way. Like if you fuse a magician that's weak physically, and one of its "parents" has a bunch of physical skills, the resulting persona won't inherit those. Something like that though I may not be 100% accurate. You can spend a ridiculous amount of time in the Velvet Room fusing many different personas many different ways. Some people are really into that aspect of these games, but for me it's just kind of a tedious chore. I try to keep my personas at/above my level, and make sure I have skills of every type (fire/wind/elec/ice/light/dark).
You're mostly right. There are a few different categories that every persona falls into and each category has different chances to inherit each type of skill. The type of skill that matches the category has an almost overwhelmingly high chance to be inherited over others, and some types of skills (like elemental opposites) can never be inherited i.e. a Fire persona will very likely inherit a Fire skill over any other and will never inherit an Ice skill. You're right that you can go really deep into it, controlling which personas get which skills to increase the likelihood you'll get your perfect inheritance of skills you want.