My friend bought a 10-y.o. Honda Jazz recently (Honda Fit in the U.S. AFAIK). Normally, after turning, the wheels should "align themselves" straight thanks to suspension geometry - in his car, you have to manually turn the wheel back for the last 15-20°. Is it possible that it was like this from factory, or is there something wrong with the front suspension?
No, it should not be like that and it came straight from the factory. Take it to the alignment shop. It's one of the things they do when they align the front end is to ensure the wheel is straight when they are done (or at least they should do that). Tell them when you take it in to have it done what's going on. Also, considering it's off as much as it is, it probably needs an alignment anyway.