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Prob not, but the University is a great place to do parkour/free running
Yes. The three major cities are Stockholm, which happens to be the capital, Gothenburg and Malmö.
yes there are, but they are not nessesary. I recommend going to www.3run.co.uk or www.urbanfreeflow.com signing up to one of the forums and asking if there is anybody in your area you could meet up with for lessons, you can only really take them in london. and only 'Parkour Generations' host them. But please please, dont PAY when you can learn from other (better) people, for free :-)
Any shoe is good for parkour; the movements are what important.
There is one called Whirlwind Parkour.
Feiyues are good for parkour, and I am not sure if they are expensive.
You do not "play" parkour; it is not like a team sport. Parkour is the freedom of movement through any and all objects (of course whatever obstacles you can overcome with your physical body); you can playfully practice and train parkour; but you do not "play" it.
Either one you prefer the most; shoes are not that big of an importance in parkour; properly learning and doing the movements is.
in any urban environment
As of now no.
Any type of shoes are good parkour; being able to the movements properly is more important.