Well, yes it's great to have separated bike lanes criss-crossing the city but still cycling here requires same amount of focus and alertness. More volumes of cyclists flowing around means one cannot always cycle abit faster, etc.
And no, locals seldom use bells. Many just cycle closely near you.
Yes of course, many don't wear helmets.
And there is a cycling map. ....but many locals consider it integrated into local transportation system. So it sounds like a strange question at times to them.
Copenhagen is the most expensive city for us on this trip--food-wise. Southern Germany was pleasantly cost-effective, especially if one buys local produce/food.