Another question on finding a dream suburb close to Stockholm ☺️

Hello welcome!, Regarding first one; check on blocket.se and hemnet.se and you also can read the Sweden guide. Google maps and sl.se will provide you with an overview of distance and transportation service level of different possible locations. And almost every school in Sweden has pretty much the same standard so to check which is good and which is not good you have to ask for statistics for last 5-10 years and make a comparison.

Regarding the second; yes the kommun you will going to be registered is obligated to stand for your children's education. The so called international school will do the needed paperwork for you.

Regarding the third; use Google and also Google translate.

Regarding the fourth; antagning.se and you will be in need of language assistance.
Cheers!

Thank you so much for your inputs. Really appreciate it ☺️

It wasn't a good answer to ask someone to google so I am going to re answer your third question again, because, perhaps that would determine more or less where to settle in Stockholm.

As far as I know residential academies don't exist in Sweden for players/students under 18 years. 

Djurgårdens IF and Hammarby IF both have Tele2 arena right next to Globen as their home grounds. Those are the elite clubs from south of Stockholm that participate the first league called "all svenskan" there are some other clubs too in southern Stockholm such as Enskede IF but to play "all svenskan" players eventually end up in one of those major clubs.

In north there is AIK they have Friends arena as their home grounds probably the oldest major league club in Stockholm, as in the south there are many other clubs too but none of them plays in the major league "all svenskan". North west there is  "Bromma Pojkarna" a club that had good potential once but don't play in all svenskan yet. (In fact I knew an Indian couple who had their son in this club)

In the west there are Assyriska FF and Syrianska FF both clubs were established by immigrants from former Assyrian empire, and both have home grounds in Södertälje and play in the major league all svenskan and actually contribute some national team players continuously.

I hope now it would be more easier for you to choose a more suitable suburb for you and your family.