Thank you all for your comments. I guess there's no need to be worried, I just need to learn how to drive a hybrid. 😄 I'll check out some videos.
About point #1: Just to clarify, I didn't mean the actual EV mode but just accelerating so lightly that the ICE doesn't kick in. By the way, is there a real use case for the EV mode in normal driving? Or is it just for showing off to your friends: "look at me, I have an electric car!". 😄 IIRC the manual mentions that it should be used if you need to be really quiet. Don't know though that in what areas you need to be that quiet but are still allowed to drive.
About point #3: I understand that the advertised figures are always quite far from the reality. However, I was a bit disappointed since my figures were rather bad even compared to more realistic Spritmonitor figures. But we'll see when I learn the most efficient way to drive. It's worth mentioning also, that my car is equipped with 215/45R17 wheels that are less fuel-efficient compared to the regular 195/65R15 (which I would prefer for other reasons as well, so I'll probably buy new rims and tires at some point).
My trips are typically somewhere between 2-15 kilometres. With really short trips it's probably never possible to get good MPG since the engine doesn't get to warm up properly, especially in the winter.