Almost all modern media depicts the "worst case scenarion" whereby arachy descends. People fight over the last remaining resources. And, to a certain extent, that is what could happen.
But if we look at many cultures, many "coming of age" used to happen around the age of 15. Additionally, for centuries, taking care of younger children has been the responsibility of slightly older siblings. A 15 year old knows a lot. If they wanted to, I imagine that a bunch of children could figure out the electricity grid before it fell apart. Many teenagers are great computer programmers....
In rural areas I would expect that the older children would simply step up to the mark and take over their parents roles of farming. Being raised on a farm you'd know much of the physical side, but probably not the business side. Thus, in the country there is the very real possibility that .... not much would happen after the initial "woah" period.
In the cities things will be a bit more dire. While some children may be able to drive, scheduled things like trains, busses and planes and much of the transport infrastructure would no longer exist. But that's not actually too much of an issue. People have used walking to get around everywhere for thousands of years. Mechanized transport is recent.
Do you think food will be an issue? Well, you've just lost some 80% of your population. While teenage boys are the hungriest [citation needed], the food requirements would drop hugely - enough for many city-dwellers to head out into the country to assist the country-dwellers to replace the normal farm workers.
So the "best case scenario" is that the people form cities migrate into the country, and, well, that's about it.
The big thing is that most books depict anarchy because it is interesting - not because it is what will happen. Case in point: disaster fiction depicts anarchy, real life shows universities forming work-teams to dig properties out of liquefaction, or nearby cities sending in resources and supplies. Many humans are friendlier than you may expect.
How long would a Walmart last having food objects inside?
A couple of weeks for dry goods (pasta, flour etc.) Meat may have to be eaten soon. If power stays on (and it likely would for at least a week or two), then up to a month. Remember, you've lost 80% of your population, so if the shop normally has stocks for a week, it now has stocks for five weeks.
What would be the governance, if any?
None, small groups are self-governing (I seem to recall that groups of ~120 tend to be crime-free as everyone will know exactly who did it). A formal governance bureaucracy would take a fair while to re-form. If all the people get put back to work farming properly, then I'd expect a feudal system to develop with the "farm kids" at the top (as they own the land, the food, and thus have the power)
How long would it take for a city/town to make its new laws?
As soon as it reaches stability, so probably six months to a year past the "event." Before then it will be a little hit-and-miss, but I suspect most kids would respect sensible practices for the first while. Many children mature very fast when responsibility is dropped on them, so the "off the rail" kids will not break society - they will stop messing around and start working. People doing real physical work to survive tend not to care about making laws.
What about the "ecosystem"?
It'll enjoy the fact that mining has stopped, that cars aren't driving and that people aren't logging forests. Many animals will find their habitats are no longer endangered by humans. Remember, the earth population has dropped from 8 billion to 2 billion....
What animals would be affected by the disappearance of adults?
Probably the ones in zoo's mostly. They'll probably die or get eaten. Hoever, nearly all poachers in Africa disappeared, so any wild animals will like it - so long as they don't start being viewed as a food resource. Pets will turn feral - many will die.
How long would medicines in a pharmacy last?
A very long time. Probably until there were adults again. I mean, seriously, how many medicines do kids take compared to the elderly?
