Absolutely. I've live in a city before where they deployed bike lanes as if all the counter was the number of kilometers. No plan whatsoever.

Yes.
If people feel like walking to the nearby shopping place is more convenient, then they will do it.

If a handheld trolley becomes socially trendy, then people will have less excuses to take a car to a nearby grocery store.
I cycling on roads at ~30km/h speeds becomes common, then most reasons for using motor vehicles get greatly reduced for most inter-city transit (specially the daily commute to work, kind).

Whenever I go cycling on the road, I feel high amounts of danger in all directions, but I still do so because I am used to it. To make more people desire using a bicycle on the roads, there needs to be a change, not only in the laws, but also the social perception towards cyclists on the road.
Rules of the road need to be made for cyclists too (there are none in my area), because the rules have an additional benefit of making traffic behaviour more predictable. This will mean that a car looking at a cyclist will know better, what action they might do next and hence, can act accordingly, instead of being as predictable as a stay cat.
Some of the things can be directly fixed by better application of technology. Right/Left indicator light with aero design easy to use controls aren't hard to make, but for some reason, are not available. I have tried cycle headlights and backlights from 3 different brands and all of them made it harder to turn it off^[2 of them required clicking and holding for over 2 seconds (which means, you can't use any of the other controls, like breaks and gear-shifts when turning off the light) and 1 required cycling through all the modes to reach the off state]. This makes it much harder to turn off the light in time when you realise you are flashing someone in the eye and should honestly not be road-legal.
Once these problems are solved, you can then consider encouraging the children to cycle around in safer areas, letting them learn cycling in a way that will be useful for running on all roads later on. This means, keeping some amount of motor-traffic in the area, but not enough to overwhelm beginners. This part is going to be a chore for the authorities.
Rules saying "always yield to cyclists" are not much more than a stopgap measure. Rules need to take into account, traffic flow and cost of braking on both sides, such that it is easier for both sides to decide optimal reactions. Stop signs that require coming to a complete stop, need to only be in places where it would be hard to see past the corner and in these cases, it should be the same for cyclists, because at higher speeds, they too are exerting, which makes it harder to notice things. For such cases, it is better to have another sign at a distance before the actual stopping point, which will also make it favourable for cars with regenerative braking. Even better, would be the use of on-road markers for both, stop signs and speed restrictions.
While there are numerical speed limits for motor vehicles, in case of cyclists there can be 3 coloured on-road markers. The lane-divider lines can have a colour code addition of white/yellow/red:

• white suggesting that the road has minimum obstacles and the cyclist can exert as much as they feel like (that is expecting that they are going under the speed limit, which would be in most cases)
• yellow suggesting that there might be some 90° merges without a traffic light, which would require vigilance, and hence the cyclist go at comfortable speeds, enabling manoeuvring
• red suggesting that the cyclist may need to stop without much leeway, in the area and hence, go slow enough depending upon their brake reaction distance. The same can be used as a prelude to a mandatory stop sign.
• It is important to make sure that at least 70% of the road be white, while only 5-10% of it be red, to make sure people will actually want to follow the guideline.

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