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Looks fun! I tried a few and they're pretty interesting-looking.

Yes, you can get some pretty funky results until you get more familiar with the right types to mix and match. But it has also given me some surprisingly good ones!
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Is there a way to get specific characteristics?
No, not in the sense you could pick blue eyes, pronounced cheekbones, etc. But you do start to get used to what sorts of features will be highlighted if you combine certain images. Plus you can re-morph an image you create and I've found that allows you some ability to emphasize certain traits (for example, if you are combining four people, then morph that image with just one other, you will get a higher percentage of the traits of the last person). I would love some sort of software that let you select specific characteristics in they way I think you are describing, but I have yet to come across any. So I've enjoyed using this to get a visual on a few of my characters!