slow growth: is almost imperceptible growth. i've had a big 2-inch marimo & 5 little nanos for 3 months, with no growth noticeable to the naked eye. :p if you get one just make sure it's the size you want because it's going to stay that size for a long long time.
splitting: the marimos are actually a kind of algae that's been rolled into a ball shape by a current, so since it's sitting on your tank floor motionless now, it wants to unroll. if you don't take them out every so often and roll them between your hands like a meatball, it won't stay in ball shape (i do this every other water change or so, maybe that's overkill but it seems to have worked so far). i've read some people saying that they just pulled off a piece of the marimo or a piece fell off, and since this is a ball of algae and not a plant with a central plant body thingus (i'm tired and don't remember the right word, you know what i mean, like a stem or root), they just rolled that piece between their hands and boom. another marimo. seems like people also often say that this leaves the marimos really lumpy then though.
fakes. "fake" marimos are moss that has been rolled around or tied or glued or whatever to a ball/rock. none of the pictures i've seen have looked like marimos at all, but whatever. they won't split into new balls, they're just mosses. i've read that the inner parts can rot and make a tank nasty after a while. there are also "fake" marimos that are totally artificial, but they're sold dry in boxes.